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Refinar búsquedaAn Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs / Mariano Giaquinta (2012)
Título : An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs Tipo de documento: documento electrónico Autores: Mariano Giaquinta ; SpringerLink (Online service) ; Luca Martinazzi Editorial: Pisa : Scuola Normale Superiore Fecha de publicación: 2012 Colección: Publications of the Scuola Normale Superiore Número de páginas: XIII, 370 p Il.: online resource ISBN/ISSN/DL: 978-88-7642-443-4 Idioma : Inglés (eng) Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the Lp theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes Nota de contenido: 1 Harmonic functions -- 2 Direct methods -- 3 Hilbert space methods -- 4 L2-regularity: the Caccioppoli inequality -- 5 Schauder estimates -- 6 Some real analysis -- 7 Lp-theory -- 8 The regularity problem in the scalar case -- 9 Partial regularity in the vector-valued case -- 10 Harmonic maps -- 11 A survey of minimal graphs En línea: http://dx.doi.org/10.1007/978-88-7642-443-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33055 An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs [documento electrónico] / Mariano Giaquinta ; SpringerLink (Online service) ; Luca Martinazzi . - Pisa : Scuola Normale Superiore, 2012 . - XIII, 370 p : online resource. - (Publications of the Scuola Normale Superiore) .
ISBN : 978-88-7642-443-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Partial differential equations Differential Equations Clasificación: 51 Matemáticas Resumen: This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the Lp theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes Nota de contenido: 1 Harmonic functions -- 2 Direct methods -- 3 Hilbert space methods -- 4 L2-regularity: the Caccioppoli inequality -- 5 Schauder estimates -- 6 Some real analysis -- 7 Lp-theory -- 8 The regularity problem in the scalar case -- 9 Partial regularity in the vector-valued case -- 10 Harmonic maps -- 11 A survey of minimal graphs En línea: http://dx.doi.org/10.1007/978-88-7642-443-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33055 Ejemplares
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Título : Colloquium De Giorgi 2010–2012 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Umberto Zannier Editorial: Pisa : Scuola Normale Superiore Fecha de publicación: 2013 Colección: Publications of the Scuola Normale Superiore num. 4 Número de páginas: Approx. 70 p Il.: online resource ISBN/ISSN/DL: 978-88-7642-457-1 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematics, general Clasificación: 51 Matemáticas Resumen: Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events Nota de contenido: Yves André: Galois theory beyond algebraic numbers and algebraic functions -- Nicholas M. Katz: Simple things we don’t know -- Endre Szemerédi: Is laziness paying off? -- Dan Abramovich: Moduli of algebraic and tropical curves -- Elias M. Stein: Three projection operators in complex analysis -- Shou-Wu Zhang: Congruent numbers and Heegner points En línea: http://dx.doi.org/10.1007/978-88-7642-457-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32643 Colloquium De Giorgi 2010–2012 [documento electrónico] / SpringerLink (Online service) ; Umberto Zannier . - Pisa : Scuola Normale Superiore, 2013 . - Approx. 70 p : online resource. - (Publications of the Scuola Normale Superiore; 4) .
ISBN : 978-88-7642-457-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematics, general Clasificación: 51 Matemáticas Resumen: Since 2001 the Scuola Normale Superiore di Pisa has organized the "Colloquio De Giorgi", a series of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general mathematical audience, and especially meant to attract graduate students and advanced undergraduate students. The lectures are intended to be not too technical, in fields of wide interest. They must provide an overview of the general topic, possibly in a historical perspective, together with a description of more recent progress. The idea of collecting the materials from these lectures and publishing them in annual volumes came out recently, as a recognition of their intrinsic mathematical interest, and also with the aim of preserving memory of these events Nota de contenido: Yves André: Galois theory beyond algebraic numbers and algebraic functions -- Nicholas M. Katz: Simple things we don’t know -- Endre Szemerédi: Is laziness paying off? -- Dan Abramovich: Moduli of algebraic and tropical curves -- Elias M. Stein: Three projection operators in complex analysis -- Shou-Wu Zhang: Congruent numbers and Heegner points En línea: http://dx.doi.org/10.1007/978-88-7642-457-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32643 Ejemplares
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Título : Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations Tipo de documento: documento electrónico Autores: Giovanni Bellettini ; SpringerLink (Online service) Editorial: Pisa : Scuola Normale Superiore Fecha de publicación: 2013 Colección: Publications of the Scuola Normale Superiore num. 12 Número de páginas: Approx. 350 p Il.: online resource ISBN/ISSN/DL: 978-88-7642-429-8 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Clasificación: 51 Matemáticas Resumen: The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems Nota de contenido: Signed distance from a smooth boundary -- Mean curvature vector and second fundamental form -- First variations of volume integrals and of the perimeter -- Smooth mean curvature flows -- Huisken’s monotonicity formula -- Inclusion principle. Local well posedness: the approach of Evans–Spruck -- Grayson’s example -- De Giorgi’s barriers -- Inner and outer regularizations -- An example of fattening -- Ilmanen’s interposition lemma -- The avoidance principle -- Comparison between barriers and a generalized evolution -- Barriers and level set evolution -- Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate En línea: http://dx.doi.org/10.1007/978-88-7642-429-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32642 Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations [documento electrónico] / Giovanni Bellettini ; SpringerLink (Online service) . - Pisa : Scuola Normale Superiore, 2013 . - Approx. 350 p : online resource. - (Publications of the Scuola Normale Superiore; 12) .
ISBN : 978-88-7642-429-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Clasificación: 51 Matemáticas Resumen: The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems Nota de contenido: Signed distance from a smooth boundary -- Mean curvature vector and second fundamental form -- First variations of volume integrals and of the perimeter -- Smooth mean curvature flows -- Huisken’s monotonicity formula -- Inclusion principle. Local well posedness: the approach of Evans–Spruck -- Grayson’s example -- De Giorgi’s barriers -- Inner and outer regularizations -- An example of fattening -- Ilmanen’s interposition lemma -- The avoidance principle -- Comparison between barriers and a generalized evolution -- Barriers and level set evolution -- Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate En línea: http://dx.doi.org/10.1007/978-88-7642-429-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32642 Ejemplares
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Título : Regularity of Optimal Transport Maps and Applications Tipo de documento: documento electrónico Autores: Guido De Philippis ; SpringerLink (Online service) Editorial: Pisa : Scuola Normale Superiore Fecha de publicación: 2013 Colección: Publications of the Scuola Normale Superiore num. 17 Número de páginas: Approx. 190 p Il.: online resource ISBN/ISSN/DL: 978-88-7642-458-8 Idioma : Inglés (eng) Palabras clave: Mathematics Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier’ theorem on existence of optimal transport maps and of Caffarelli’s Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero En línea: http://dx.doi.org/10.1007/978-88-7642-458-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32644 Regularity of Optimal Transport Maps and Applications [documento electrónico] / Guido De Philippis ; SpringerLink (Online service) . - Pisa : Scuola Normale Superiore, 2013 . - Approx. 190 p : online resource. - (Publications of the Scuola Normale Superiore; 17) .
ISBN : 978-88-7642-458-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Calculus of variations Variations and Optimal Control; Optimization Clasificación: 51 Matemáticas Resumen: In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier’ theorem on existence of optimal transport maps and of Caffarelli’s Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero En línea: http://dx.doi.org/10.1007/978-88-7642-458-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32644 Ejemplares
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Título : The Search for the Higgs Boson at CMS Tipo de documento: documento electrónico Autores: Giovanni Petrucciani ; SpringerLink (Online service) Editorial: Pisa : Scuola Normale Superiore Fecha de publicación: 2013 Colección: Publications of the Scuola Normale Superiore num. 18 Número de páginas: Approx. 200 p Il.: online resource ISBN/ISSN/DL: 978-88-7642-482-3 Idioma : Inglés (eng) Palabras clave: Physics Nuclear physics Particle and Clasificación: 51 Matemáticas Resumen: This book describes the searches that lead to the discovery of a Higgs boson performed at CMS, one of the two main experiments at the CERN LHC. After an overview of the theory and of the CMS experiment, all search channels are described, with emphasis on the ones with the best sensitivity. The statistical methodology used to analyse and the outcomes of the searches and the discovery results are then presented in detail Nota de contenido: The standard model of elementary particles and the Higgs boson -- The CMS experiment at the CERN LHC.- Searches for a Higgs boson at CMS, in the different final states -- Statistical analysis for Higgs boson searches -- Results En línea: http://dx.doi.org/10.1007/978-88-7642-482-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32647 The Search for the Higgs Boson at CMS [documento electrónico] / Giovanni Petrucciani ; SpringerLink (Online service) . - Pisa : Scuola Normale Superiore, 2013 . - Approx. 200 p : online resource. - (Publications of the Scuola Normale Superiore; 18) .
ISBN : 978-88-7642-482-3
Idioma : Inglés (eng)
Palabras clave: Physics Nuclear physics Particle and Clasificación: 51 Matemáticas Resumen: This book describes the searches that lead to the discovery of a Higgs boson performed at CMS, one of the two main experiments at the CERN LHC. After an overview of the theory and of the CMS experiment, all search channels are described, with emphasis on the ones with the best sensitivity. The statistical methodology used to analyse and the outcomes of the searches and the discovery results are then presented in detail Nota de contenido: The standard model of elementary particles and the Higgs boson -- The CMS experiment at the CERN LHC.- Searches for a Higgs boson at CMS, in the different final states -- Statistical analysis for Higgs boson searches -- Results En línea: http://dx.doi.org/10.1007/978-88-7642-482-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32647 Ejemplares
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