The Eigenvalue Problem Of The P Laplacian In Metric Spaces
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The Eigenvalue Problem Of The P Laplacian In Metric Spaces
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Author : Mikko Pere
language : en
Publisher:
Release Date : 2004
The Eigenvalue Problem Of The P Laplacian In Metric Spaces written by Mikko Pere and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Eigenvalues categories.
Handbook Of Applied Analysis
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Author : Nikolaos S. Papageorgiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-31
Handbook Of Applied Analysis written by Nikolaos S. Papageorgiou 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 2009-05-31 with Mathematics categories.
Accurate models to describe real-world phenomena are indispensable for research in such scientific fields as physics, engineering, biology, chemistry, and economics. The tools and techniques of applied analysis facilitate the development of mathematical models and can thereby serve as an excellent resource for students and researchers in various scientific and mathematical disciplines. This self-contained, comprehensive handbook provides an in-depth examination of important theoretical methods and procedures in applied analysis. Unique features of the Handbook of Applied Analysis: • Presents an accessible introduction to modern analysis, while still serving as a useful reference for researchers and practitioners; • Covers a large number of diverse topics: smooth and nonsmooth differential calculus, optimal control, fixed point theory, critical point theory, linear and nonlinear eigenvalue problems, nonlinear boundary value problems, set-valued analysis, game theory, stochastic analysis, and evolutionary equations; • Serves as a complete guide to the theory of nonlinear analysis; • Includes numerous examples that demonstrate and expand upon the topics presented; • Suggests many directions for further research and study. In this one volume, the reader can find many of the most important theoretical trends in nonlinear analysis and applications to different fields. These features, together with an extensive bibliography, make the volume a valuable tool for every researcher working on nonlinear analysis.
Nonlinear Potential Theory On Metric Spaces
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Author : Anders Björn
language : en
Publisher: European Mathematical Society
Release Date : 2011
Nonlinear Potential Theory On Metric Spaces written by Anders Björn and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Asymptotical Behaviour Of A Semilinear Diffusion Equation
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Author : Ville Ramula
language : en
Publisher:
Release Date : 2006
Asymptotical Behaviour Of A Semilinear Diffusion Equation written by Ville Ramula and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations, Nonlinear categories.
Inverse Problems For Nonsmooth First Order Perturbations Of The Laplacian
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Author : Mikko Salo
language : en
Publisher:
Release Date : 2004
Inverse Problems For Nonsmooth First Order Perturbations Of The Laplacian written by Mikko Salo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Inverse problems (Differential equations) categories.
Variational And Diffusion Problems In Random Walk Spaces
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Author : José M. Mazón
language : en
Publisher: Springer Nature
Release Date : 2023-08-04
Variational And Diffusion Problems In Random Walk Spaces written by José M. Mazón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-04 with Mathematics categories.
This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research. Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.
Differential Operators On Spaces Of Variable Integrability
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Author : Osvaldo Mendez
language : en
Publisher: World Scientific
Release Date : 2014-06-26
Differential Operators On Spaces Of Variable Integrability written by Osvaldo Mendez and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Mathematics categories.
The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics.
Heat Kernels And Analysis On Manifolds Graphs And Metric Spaces
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Author : Pascal Auscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Heat Kernels And Analysis On Manifolds Graphs And Metric Spaces written by Pascal Auscher 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 2003 with Mathematics categories.
This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Spectral Geometry Of The Laplacian Spectral Analysis And Differential Geometry Of The Laplacian
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Author : Hajime Urakawa
language : en
Publisher: World Scientific
Release Date : 2017-06-02
Spectral Geometry Of The Laplacian Spectral Analysis And Differential Geometry Of The Laplacian written by Hajime Urakawa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-02 with Mathematics categories.
The totality of the eigenvalues of the Laplacian of a compact Riemannian manifold is called the spectrum. We describe how the spectrum determines a Riemannian manifold. The continuity of the eigenvalue of the Laplacian, Cheeger and Yau's estimate of the first eigenvalue, the Lichnerowicz-Obata's theorem on the first eigenvalue, the Cheng's estimates of the kth eigenvalues, and Payne-Pólya-Weinberger's inequality of the Dirichlet eigenvalue of the Laplacian are also described. Then, the theorem of Colin de Verdière, that is, the spectrum determines the totality of all the lengths of closed geodesics is described. We give the V Guillemin and D Kazhdan's theorem which determines the Riemannian manifold of negative curvature.