Download or read book Boundary Value Problems and Hardy Spaces for Elliptic Systems with Block Structure written by Pascal Auscher and published by Springer Nature. This book was released on 2023-08-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Elliptic Boundary Value Problems with Fractional Regularity Data The First Order Approach written by Alex Amenta and published by American Mathematical Soc.. This book was released on 2018-04-03 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Boundary Value Problems for Elliptic Systems written by J. T. Wloka and published by Cambridge University Press. This book was released on 1995-07-28 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Integro Differential Elliptic Equations written by Xavier Fernández-Real and published by Springer Nature. This book was released on with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Boundary Value Problems for Elliptic Equations and Systems written by Guo Chun Wen and published by Longman Scientific and Technical. This book was released on 1990 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Boundary Value Problems Governed by Second Order Elliptic Systems written by David L. Clements and published by Pitman Advanced Publishing Program. This book was released on 1981 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Elliptic Systems in the Plane written by Wolfgang L. Wendland and published by Pitman Publishing. This book was released on 1979 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonlinear Elliptic Boundary Value Problems and Their Applications written by H Begehr and published by CRC Press. This book was released on 1996-05-15 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Boundary value Problems with Free Boundaries for Elliptic Systems of Equations written by Valentin Nikolaevich Monakhov and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Layer Potentials and Boundary Value Problems for Second Order Elliptic Operators with Data in Besov Spaces written by Ariel Barton: and published by American Mathematical Soc.. This book was released on 2016-09-06 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Harmonic Analysis and Boundary Value Problems written by Luca Capogna and published by American Mathematical Soc.. This book was released on 2001-01-01 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Lectures on Elliptic Boundary Value Problems written by Shmuel Agmon and published by . This book was released on 1965 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Elliptic Boundary Value Problems in the Spaces of Distributions written by Y. Roitberg and published by . This book was released on 2014-01-15 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1524 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Boundary Value Problems for Second Order Elliptic Equations written by A. V. Bicadze and published by . This book was released on 1963 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bernoulli Free Boundary Problems written by Eugene Shargorodsky and published by American Mathematical Soc.. This book was released on 2008 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions of existence, multiplicity, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems. In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable.

Download or read book Physics Briefs written by and published by . This book was released on 1990 with total page 1354 pages. Available in PDF, EPUB and Kindle. Book excerpt: