Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems
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Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems
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Author : Carlos E. Kenig
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig 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 1994 with Mathematics categories.
In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.
Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems
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Author : Carlos E. Kenig
language : en
Publisher:
Release Date : 1994
Harmonic Analysis Techniques For Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Boundary value problems categories.
In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result migh.
Multi Layer Potentials And Boundary Problems
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Author : Irina Mitrea
language : en
Publisher: Springer
Release Date : 2013-01-05
Multi Layer Potentials And Boundary Problems written by Irina Mitrea and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-05 with Mathematics categories.
Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Calderón, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatment based on this approach. This research monograph lays, for the first time, the mathematical foundation aimed at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including layer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions, boundary value problems with data in Whitney–Lebesque spaces, Whitney–Besov spaces, Whitney–Sobolev- based Lebesgue spaces, Whitney–Triebel–Lizorkin spaces,Whitney–Sobolev-based Hardy spaces, Whitney–BMO and Whitney–VMO spaces.
Elliptic Boundary Value Problems With Fractional Regularity Data The First Order Approach
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Author : Alex Amenta
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-04-03
Elliptic Boundary Value Problems With Fractional Regularity Data The First Order Approach written by Alex Amenta 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 2018-04-03 with Boundary value problems categories.
A co-publication of the AMS and Centre de Recherches Mathématiques In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The authors use the so-called “first order approach” which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.
Harmonic Analysis And Boundary Value Problems
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Author : Luca Capogna
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-01-01
Harmonic Analysis And Boundary Value Problems written by Luca Capogna 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 2001-01-01 with Mathematics categories.
This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ''Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ''two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.
Boundary Value Problems And Markov Processes
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Author : Kazuaki Taira
language : en
Publisher:
Release Date : 1991
Boundary Value Problems And Markov Processes written by Kazuaki Taira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Boundary value problems categories.
Harmonic Analysis And Boundary Value Problems
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Author : Luca Capogna
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Harmonic Analysis And Boundary Value Problems written by Luca Capogna 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 2001 with Mathematics categories.
This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ``two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.
Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science
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Author : Isaac Pesenson
language : en
Publisher: Birkhäuser
Release Date : 2017-08-09
Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science written by Isaac Pesenson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-09 with Mathematics categories.
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
Layer Potentials And Boundary Value Problems For Second Order Elliptic Operators With Data In Besov Spaces
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Author : Ariel Barton:
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-06
Layer Potentials And Boundary Value Problems For Second Order Elliptic Operators With Data In Besov Spaces written by Ariel Barton: 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 2016-09-06 with Besov space categories.
This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Lp classes. The authors establish: (1) Mapping properties for the double and single layer potentials, as well as the Newton potential; (2) Extrapolation-type solvability results: the fact that solvability of the Dirichlet or Neumann boundary value problem at any given Lp space automatically assures their solvability in an extended range of Besov spaces; (3) Well-posedness for the non-homogeneous boundary value problems. In particular, the authors prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric, coefficients.
Polyharmonic Boundary Value Problems
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Author : Filippo Gazzola
language : en
Publisher: Springer
Release Date : 2010-05-26
Polyharmonic Boundary Value Problems written by Filippo Gazzola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-26 with Mathematics categories.
This accessible monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. It provides rapid access to recent results and references.