Stability In Gagliardo Nirenberg Sobolev Inequalities Flows Regularity And The Entropy Method
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Stability In Gagliardo Nirenberg Sobolev Inequalities Flows Regularity And The Entropy Method
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Author : Matteo Bonforte
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-29
Stability In Gagliardo Nirenberg Sobolev Inequalities Flows Regularity And The Entropy Method written by Matteo Bonforte and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-29 with Mathematics categories.
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Geometric And Analytic Aspects Of Functional Variational Principles
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Author : Rupert Frank
language : en
Publisher: Springer Nature
Release Date : 2024-11-19
Geometric And Analytic Aspects Of Functional Variational Principles written by Rupert Frank and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-19 with Mathematics categories.
This book is dedicated to exploring optimization problems of geometric-analytic nature, which are fundamental to tackling various unresolved questions in mathematics and physics. These problems revolve around minimizing geometric or analytic quantities, often representing physical energies, within prescribed collections of sets or functions. They serve as catalysts for advancing methodologies in calculus of variations, partial differential equations, and geometric analysis. Furthermore, insights from optimal functional-geometric inequalities enhance analytical problem-solving endeavors. The contributions focus on the intricate interplay between these inequalities and problems of differential and variational nature. Key topics include functional and geometric inequalities, optimal norms, sharp constants in Sobolev-type inequalities, and the regularity of solutions to variational problems. Readers will gain a comprehensive understanding of these concepts, deepening their appreciation for their relevance in mathematical and physical inquiries.
Analysis And Geometry Of Markov Diffusion Operators
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Author : Dominique Bakry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-18
Analysis And Geometry Of Markov Diffusion Operators written by Dominique Bakry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-18 with Mathematics categories.
The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic.
A First Course In Sobolev Spaces
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Author : Giovanni Leoni
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-17
A First Course In Sobolev Spaces written by Giovanni Leoni and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-17 with Mathematics categories.
This book is about differentiation of functions. It is divided into two parts, which can be used as different textbooks, one for an advanced undergraduate course in functions of one variable and one for a graduate course on Sobolev functions. The first part develops the theory of monotone, absolutely continuous, and bounded variation functions of one variable and their relationship with Lebesgue–Stieltjes measures and Sobolev functions. It also studies decreasing rearrangement and curves. The second edition includes a chapter on functions mapping time into Banach spaces. The second part of the book studies functions of several variables. It begins with an overview of classical results such as Rademacher's and Stepanoff's differentiability theorems, Whitney's extension theorem, Brouwer's fixed point theorem, and the divergence theorem for Lipschitz domains. It then moves to distributions, Fourier transforms and tempered distributions. The remaining chapters are a treatise on Sobolev functions. The second edition focuses more on higher order derivatives and it includes the interpolation theorems of Gagliardo and Nirenberg. It studies embedding theorems, extension domains, chain rule, superposition, Poincaré's inequalities and traces. A major change compared to the first edition is the chapter on Besov spaces, which are now treated using interpolation theory.
Degenerate Parabolic Equations
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Author : Emmanuele DiBenedetto
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Degenerate Parabolic Equations written by Emmanuele DiBenedetto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Gradient Flows
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Author : Luigi Ambrosio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-29
Gradient Flows written by Luigi Ambrosio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-29 with Mathematics categories.
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Functional Inequalities New Perspectives And New Applications
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Author : Nassif Ghoussoub
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-09
Functional Inequalities New Perspectives And New Applications written by Nassif Ghoussoub and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.
Free Boundary Problems In Continuum Mechanics
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Author : S.N. Antontsev
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07
Free Boundary Problems In Continuum Mechanics written by S.N. Antontsev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Social Science categories.
Progress in different fields of mechanics, such as filtra tion theory, elastic-plastic problems, crystallization pro cesses, internal and surface waves, etc., is governed to a great extent by the advances in the study of free boundary problems for nonlinear partial differential equations. Free boundary problems form a scientific area which attracts attention of many specialists in mathematics and mechanics. Increasing interest in the field has given rise to the "International Conferences on Free Boundary Problems and Their Applications" which have convened, since the 1980s, in such countries as England, the United states, Italy, France and Germany. This book comprises the papers presented at the Interna tional Conference "Free Boundary Problems in Continuum Mechanics", organized by the Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, July 15-19, 1991, Novosibirsk, Russia. The scientific committee consisted of: Co-chairmen: K.-H. Hoffmann, L.V. Ovsiannikov S. Antontsev (Russia) J. Ockendon (UK) M. Fremond (France) L. Ovsiannikov (Russia) A. Friedman (USA) S. Pokhozhaev (Russia) K.-H. Hoffmann (Germany) M. Primicerio (Italy) A. Khludnev (Russia) V. Pukhnachov (Russia) V. Monakhov (Russia) Yu. Shokin (Russia) V. Teshukov (Russia) Our thanks are due to the members of the Scientific Com mittee, all authors, and participants for contributing to the success of the Conference. We would like to express special appreciation to N. Makarenko, J. Mal'tseva and T. Savelieva, Lavrentyev Institute of Hydrodynamics, for their help in preparing this book for publication
Isoperimetric Inequalities In Mathematical Physics Am 27 Volume 27
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Author : G. Polya
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Isoperimetric Inequalities In Mathematical Physics Am 27 Volume 27 written by G. Polya and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM-27), Volume 27, will be forthcoming.
Entropy Methods For Diffusive Partial Differential Equations
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Author : Ansgar Jüngel
language : en
Publisher: Springer
Release Date : 2016-06-17
Entropy Methods For Diffusive Partial Differential Equations written by Ansgar Jüngel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-17 with Mathematics categories.
This book presents a range of entropy methods for diffusive PDEs devised by many researchers in the course of the past few decades, which allow us to understand the qualitative behavior of solutions to diffusive equations (and Markov diffusion processes). Applications include the large-time asymptotics of solutions, the derivation of convex Sobolev inequalities, the existence and uniqueness of weak solutions, and the analysis of discrete and geometric structures of the PDEs. The purpose of the book is to provide readers an introduction to selected entropy methods that can be found in the research literature. In order to highlight the core concepts, the results are not stated in the widest generality and most of the arguments are only formal (in the sense that the functional setting is not specified or sufficient regularity is supposed). The text is also suitable for advanced master and PhD students and could serve as a textbook for special courses and seminars.