Elliptic Theory For Sets With Higher Co Dimensional Boundaries
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Elliptic Theory For Sets With Higher Co Dimensional Boundaries
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Author : Guy David
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-30
Elliptic Theory For Sets With Higher Co Dimensional Boundaries written by Guy David 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 2021-12-30 with Mathematics categories.
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Rectifiability
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Author : Pertti Mattila
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-12
Rectifiability written by Pertti Mattila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-12 with Mathematics categories.
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside.
Elliptic Theory In Domains With Boundaries Of Mixed Dimension
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Author : GUY. DAVID
language : en
Publisher:
Release Date : 2023
Elliptic Theory In Domains With Boundaries Of Mixed Dimension written by GUY. DAVID and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Index Theory Of Elliptic Boundary Problems
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Author : Stephan Rempel
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1982-12-31
Index Theory Of Elliptic Boundary Problems written by Stephan Rempel and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-12-31 with Mathematics categories.
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Linear Second Order Elliptic Operators
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Author : Julián López-Gómez
language : en
Publisher: World Scientific Publishing Company
Release Date : 2013-04-24
Linear Second Order Elliptic Operators written by Julián López-Gómez and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-24 with Science categories.
The main goal of the book is to provide a comprehensive and self-contained proof of the, relatively recent, theorem of characterization of the strong maximum principle due to Molina-Meyer and the author, published in Diff. Int. Eqns. in 1994, which was later refined by Amann and the author in a paper published in J. of Diff. Eqns. in 1998. Besides this characterization has been shown to be a pivotal result for the development of the modern theory of spatially heterogeneous nonlinear elliptic and parabolic problems; it has allowed us to update the classical theory on the maximum and minimum principles by providing with some extremely sharp refinements of the classical results of Hopf and Protter-Weinberger. By a celebrated result of Berestycki, Nirenberg and Varadhan, Comm. Pure Appl. Maths. in 1994, the characterization theorem is partially true under no regularity constraints on the support domain for Dirichlet boundary conditions. Instead of encyclopedic generality, this book pays special attention to completeness, clarity and transparency of its exposition so that it can be taught even at an advanced undergraduate level. Adopting this perspective, it is a textbook; however, it is simultaneously a research monograph about the maximum principle, as it brings together for the first time in the form of a book, the most paradigmatic classical results together with a series of recent fundamental results scattered in a number of independent papers by the author of this book and his collaborators. Chapters 3, 4, and 5 can be delivered as a classical undergraduate, or graduate, course in Hilbert space techniques for linear second order elliptic operators, and Chaps. 1 and 2 complete the classical results on the minimum principle covered by the paradigmatic textbook of Protter and Weinberger by incorporating some recent classification theorems of supersolutions by Walter, 1989, and the author, 2003. Consequently, these five chapters can be taught at an undergraduate, or graduate, level. Chapters 6 and 7 study the celebrated theorem of Krein–Rutman and infer from it the characterizations of the strong maximum principle of Molina-Meyer and Amann, in collaboration with the author, which have been incorporated to a textbook by the first time here, as well as the results of Chaps. 8 and 9, polishing some recent joint work of Cano-Casanova with the author. Consequently, the second half of the book consists of a more specialized monograph on the maximum principle and the underlying principal eigenvalues.
Elliptic Operators And Lie Groups
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Author : Derek W. Robinson
language : en
Publisher:
Release Date : 1991
Elliptic Operators And Lie Groups written by Derek W. Robinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Elliptic operators arise naturally in several different mathematical settings, notably in the representation theory of Lie groups, the study of evolution equations, and the examination of Riemannian manifolds. This book develops the basic theory of elliptic operators on Lie groups and thereby extends the conventional theory of parabolic evolution equations to a natural noncommutative context. In order to achieve this goal, the author presents a synthesis of ideas from partial differential equations, harmonic analysis, functional analysis, and the theory of Lie groups. He begins by discussing the abstract theory of general operators with complex coefficients before concentrating on the central case of second-order operators with real coefficients. A full discussion of second-order subelliptic operators is also given. Prerequisites are a familiarity with basic semigroup theory, the elementary theory of Lie groups, and a firm grounding in functional analysis as might be gained from the first year of a graduate course.
Elliptic Operators Topology And Asymptotic Methods
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Author : John Roe
language : en
Publisher: Longman Scientific and Technical
Release Date : 1988
Elliptic Operators Topology And Asymptotic Methods written by John Roe and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Multidimensional Complex Analysis And Partial Differential Equations
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Author : Francois Treves
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Multidimensional Complex Analysis And Partial Differential Equations written by Francois Treves 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 1997 with Analyse fonctionnelle - Congrès categories.
This collection of papers by outstanding contributors in analysis, partial differential equations and several complex variables is dedicated to Professor Treves in honour of his 65th birthday. There are five excellent survey articles covering analytic singularities, holomorphically nondegenerate algebraic hypersurfaces, analyticity of CR mappings, removable singularities of vector fields and local solvability for systems of vector fields. The other papers are original research contributions on topics such as Klein-Gordon and Dirac equations, Toeplitz operators, elliptic structures, complexification of Lie groups, and pseudo-differential operators.
Elliptic Problems In Domains With Piecewise Smooth Boundaries
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Author : Sergey Nazarov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-01
Elliptic Problems In Domains With Piecewise Smooth Boundaries written by Sergey Nazarov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
An Introduction To The Regularity Theory For Elliptic Systems Harmonic Maps And Minimal Graphs
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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30
An Introduction To The Regularity Theory For Elliptic Systems Harmonic Maps And Minimal Graphs written by Mariano Giaquinta 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 2013-07-30 with Mathematics categories.
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 L^p-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 L^p theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.