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Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems

1994 Mathematics
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Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 093/5 ( reviews)

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Book Synopsis Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems by : Carlos E. Kenig

Download or read book Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: 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

1994 Boundary value problems
Download Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems PDF Online Free

Author :
Release : 1994
Genre : Boundary value problems
Kind : eBook
Book Rating : 435/5 ( reviews)

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Book Synopsis Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems by : Carlos E. Kenig

Download or read book Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems written by Carlos E. Kenig. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic Analysis and Boundary Value Problems

2001 Mathematics
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Release : 2001
Genre : Mathematics
Kind : eBook
Book Rating : 456/5 ( reviews)

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Book Synopsis Harmonic Analysis and Boundary Value Problems by : Luca Capogna

Download or read book Harmonic Analysis and Boundary Value Problems written by Luca Capogna. This book was released on 2001. 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.

Multi-Layer Potentials and Boundary Problems

2013-01-05 Mathematics
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Release : 2013-01-05
Genre : Mathematics
Kind : eBook
Book Rating : 668/5 ( reviews)

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Book Synopsis Multi-Layer Potentials and Boundary Problems by : Irina Mitrea

Download or read book Multi-Layer Potentials and Boundary Problems written by Irina Mitrea. This book was released on 2013-01-05. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometric Harmonic Analysis V

2023-08-22 Mathematics
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Release : 2023-08-22
Genre : Mathematics
Kind : eBook
Book Rating : 618/5 ( reviews)

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Book Synopsis Geometric Harmonic Analysis V by : Dorina Mitrea

Download or read book Geometric Harmonic Analysis V written by Dorina Mitrea. This book was released on 2023-08-22. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.

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