Boundary Value Problems And Hardy Spaces For Elliptic Systems With Block Structure
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Boundary Value Problems And Hardy Spaces For Elliptic Systems With Block Structure
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Author : Pascal Auscher
language : en
Publisher: Springer Nature
Release Date : 2023-08-28
Boundary Value Problems And Hardy Spaces For Elliptic Systems With Block Structure written by Pascal Auscher and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-28 with Mathematics categories.
In this monograph, for elliptic systems with block structure in the upper half-space and t-independent coefficients, the authors settle the study of boundary value problems by proving compatible well-posedness of Dirichlet, regularity and Neumann problems in optimal ranges of exponents. Prior to this work, only the two-dimensional situation was fully understood. In higher dimensions, partial results for existence in smaller ranges of exponents and for a subclass of such systems had been established. The presented uniqueness results are completely new, and the authors also elucidate optimal ranges for problems with fractional regularity data. The first part of the monograph, which can be read independently, provides optimal ranges of exponents for functional calculus and adapted Hardy spaces for the associated boundary operator. Methods use and improve, with new results, all the machinery developed over the last two decades to study such problems: the Kato square root estimates and Riesz transforms, Hardy spaces associated to operators, off-diagonal estimates, non-tangential estimates and square functions, and abstract layer potentials to replace fundamental solutions in the absence of local regularity of solutions.
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.
Boundary Value Problems For Elliptic Systems
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Author : J. T. Wloka
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-28
Boundary Value Problems For Elliptic Systems written by J. T. Wloka 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 1995-07-28 with Mathematics categories.
The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators, and matrix analysis.
Integro Differential Elliptic Equations
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Author : Xavier Fernández-Real
language : en
Publisher: Springer Nature
Release Date :
Integro Differential Elliptic Equations written by Xavier Fernández-Real and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Boundary Value Problems For Elliptic Equations And Systems
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Author : Guo Chun Wen
language : en
Publisher: Longman Scientific and Technical
Release Date : 1990
Boundary Value Problems For Elliptic Equations And Systems written by Guo Chun Wen 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 1990 with Boundary value problems categories.
Boundary Value Problems Governed By Second Order Elliptic Systems
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Author : David L. Clements
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1981
Boundary Value Problems Governed By Second Order Elliptic Systems written by David L. Clements and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
Elliptic Systems In The Plane
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Author : Wolfgang L. Wendland
language : en
Publisher: Pitman Publishing
Release Date : 1979
Elliptic Systems In The Plane written by Wolfgang L. Wendland and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.
Nonlinear Elliptic Boundary Value Problems And Their Applications
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Author : H Begehr
language : en
Publisher: CRC Press
Release Date : 1996-05-15
Nonlinear Elliptic Boundary Value Problems And Their Applications written by H Begehr and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-15 with Mathematics categories.
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.
Boundary Value Problems With Free Boundaries For Elliptic Systems Of Equations
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Author : Valentin Nikolaevich Monakhov
language : en
Publisher:
Release Date : 1983
Boundary Value Problems With Free Boundaries For Elliptic Systems Of Equations written by Valentin Nikolaevich Monakhov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Boundary value problems categories.
This book is concerned with certain classes of nonlinear problems for elliptic systems of partial differential equations: boundary-value problems with free boundaries. The first part has to do with the general theory of boundary-value problems for analytic functions and its applications to hydrodynamics. The second presents the theory of quasiconformal mappings, along with the theory of boundary-value problems for elliptic systems of equations and applications of it to problems in the mechanics of continuous media with free boundaries: problems in subsonic gas dynamics, filtration theory, and.