Singular Integral Operators Quantitative Flatness And Boundary Problems

Author : Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Unknown
Page : 0 pages
File Size : 46,6 Mb
Release : 2022
Category : Electronic
ISBN : 3031082354

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Singular Integral Operators, Quantitative Flatness, and Boundary Problems by Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems - as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis - will find this text to be a valuable addition to the mathematical literature.

Author : Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 605 pages
File Size : 42,6 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9783031082344

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Singular Integral Operators, Quantitative Flatness, and Boundary Problems by Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.

Author : F. D. Gakhov
Publisher : Courier Corporation
Page : 596 pages
File Size : 40,9 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0486662756

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Boundary Value Problems by F. D. Gakhov Pdf

A brilliant monograph, directed to graduate and advanced-undergraduate students, on the theory of boundary value problems for analytic functions and its applications to the solution of singular integral equations with Cauchy and Hilbert kernels. With exercises.

Author : Christian Constanda,Bardo E.J. Bodmann,Paul J. Harris
Publisher : Springer Nature
Page : 407 pages
File Size : 51,6 Mb
Release : 2023-10-31
Category : Mathematics
ISBN : 9783031340994

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Integral Methods in Science and Engineering by Christian Constanda,Bardo E.J. Bodmann,Paul J. Harris Pdf

This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.

Author : Fedor Dmitrievich Gakhov
Publisher : Unknown
Page : 594 pages
File Size : 51,6 Mb
Release : 1966
Category : Boundary value problems
ISBN : UOM:39015000982853

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Boundary Value Problems by Fedor Dmitrievich Gakhov Pdf

Author : S. G. Mikhlin,S. Prössdorf
Publisher : Walter de Gruyter GmbH & Co KG
Page : 528 pages
File Size : 42,9 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 9783112719152

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Singular Integral Operators by S. G. Mikhlin,S. Prössdorf Pdf

Keine ausführliche Beschreibung für "Singular Integral Operators" verfügbar.

Author : Vladimír Sládek,Ján Sládek
Publisher : Computational Mechanics
Page : 456 pages
File Size : 47,5 Mb
Release : 1998
Category : Mathematics
ISBN : STANFORD:36105023115822

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Singular Integrals in Boundary Element Methods by Vladimír Sládek,Ján Sládek Pdf

A text in singular integrals in boundary element methods. Topics covered include: treatment in crack problems; regularization of boundary integral equations by the derivative transfer method; regularization and evaluation of singular domain integrals in boundary element methods and others.

Author : Alexander Volberg
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 40,7 Mb
Release : 2003
Category : Calderón-Zygmund operator
ISBN : 9780821832523

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Calderon-Zygmund Capacities and Operators on Nonhomogeneous Spaces by Alexander Volberg Pdf

Singular integral operators play a central role in modern harmonic analysis. Simplest examples of singular kernels are given by Calderon-Zygmund kernels. Many important properties of singular integrals have been thoroughly studied for Calderon-Zygmund operators. In the 1980's and early 1990's, Coifman, Weiss, and Christ noticed that the theory of Calderon-Zygmund operators can be generalized from Euclidean spaces to spaces of homogeneous type. The purpose of this book is to make the reader believe that homogeneity (previously considered as a cornerstone of the theory) is not needed. This claim is illustrated by presenting two harmonic analysis problems famous for their difficulty. The first problem treats semiadditivity of analytic and Lipschitz harmonic capacities. The volume presents the first self-contained and unified proof of the semiadditivity of these capacities. The book details Tolsa's solution of Painleve's and Vitushkin's problems and explains why these are problems of the theory of Calderon-Zygmund operators on nonhomogeneous spaces. The exposition is not dimension-specific, which allows the author to treat Lipschitz harmonic capacity and analytic capacity at the same time. The second problem considered in the volume is a two-weight estimate for the Hilbert transform. This problem recently found important applications in operator theory, where it is intimately related to spectral theory of small perturbations of unitary operators. The book presents a technique that can be helpful in overcoming rather bad degeneracies (i.e., exponential growth or decay) of underlying measure (volume) on the space where the singular integral operator is considered. These situations occur, for example, in boundary value problems for elliptic PDE's in domains with extremely singular boundaries. Another example involves harmonic analysis on the boundaries of pseudoconvex domains that goes beyond the scope of Carnot-Caratheodory spaces. The book is suitable for graduate students and research mathematicians interested in harmonic analysis.

Author : N. I. Muskhelishvili,J. R. M. Radok
Publisher : Courier Corporation
Page : 466 pages
File Size : 45,8 Mb
Release : 2008-01-01
Category : Science
ISBN : 9780486462424

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Singular Integral Equations by N. I. Muskhelishvili,J. R. M. Radok Pdf

This high-level treatment considers one-dimensional singular integral equations involving Cauchy principal values, covering Hölder condition, Hilbert and Riemann-Hilbert problems, Dirichlet problems, inversion formulas for arcs, more. 1992 edition.

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 1006 pages
File Size : 41,9 Mb
Release : 2023-08-22
Category : Mathematics
ISBN : 9783031315619

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Geometric Harmonic Analysis V by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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.

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 980 pages
File Size : 55,8 Mb
Release : 2023-05-12
Category : Mathematics
ISBN : 9783031227356

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Geometric Harmonic Analysis III by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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. Volume III is concerned with integral representation formulas for nullsolutions of elliptic PDEs, Calderón-Zygmund theory for singular integral operators, Fatou type theorems for systems of elliptic PDEs, and applications to acoustic and electromagnetic scattering. Overall, this amounts to a powerful and nuanced theory developed on uniformly rectifiable sets, which builds on the work of many predecessors.

Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 1004 pages
File Size : 41,5 Mb
Release : 2023-07-09
Category : Mathematics
ISBN : 9783031291791

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Geometric Harmonic Analysis IV by Dorina Mitrea,Irina Mitrea,Marius Mitrea Pdf

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. Traditionally, the label “Calderón-Zygmund theory” has been applied to a distinguished body of works primarily pertaining to the mapping properties of singular integral operators on Lebesgue spaces, in various geometric settings. Volume IV amounts to a versatile Calderón-Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries, considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.

Author : Alberto P. Calderón
Publisher : Unknown
Page : 394 pages
File Size : 46,9 Mb
Release : 1967
Category : Integral equations
ISBN : UCSD:31822028821916

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Singular Integrals by Alberto P. Calderón Pdf

Author : Marius Mitrea
Publisher : Springer
Page : 0 pages
File Size : 52,8 Mb
Release : 1994-04-28
Category : Mathematics
ISBN : 3540578846

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Clifford Wavelets, Singular Integrals, and Hardy Spaces by Marius Mitrea Pdf

The book discusses the extensions of basic Fourier Analysis techniques to the Clifford algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces, Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results are applied to potential theory and elliptic boundary value problems on non-smooth domains. The book is self-contained to a large extent and well-suited for graduate students and researchers in the areas of wavelet theory, Harmonic and Clifford Analysis. It will also interest the specialists concerned with the applications of the Clifford algebra machinery to Mathematical Physics.

Author : Fedor Dmitrievič Gachov
Publisher : Unknown
Page : 561 pages
File Size : 53,7 Mb
Release : 1969
Category : Electronic
ISBN : OCLC:67414409

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Boundary Value Problems by Fedor Dmitrievič Gachov Pdf