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ISBN: 9783642326653
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 differen… mais…
2013, ISBN: 364232665X
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2013, ISBN: 9783642326653
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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 an
Dados detalhados do livro - Multi-Layer Potentials and Boundary Problems
EAN (ISBN-13): 9783642326653
ISBN (ISBN-10): 364232665X
Livro de capa dura
Livro de bolso
Ano de publicação: 2013
Editor/Editora: Springer Berlin
Livro na base de dados desde 2014-03-17T03:31:35-03:00 (Sao Paulo)
Página de detalhes modificada pela última vez em 2022-05-02T08:56:03-03:00 (Sao Paulo)
Número ISBN/EAN: 9783642326653
Número ISBN - Ortografia alternativa:
3-642-32665-X, 978-3-642-32665-3
Ortografia alternativa e termos de pesquisa relacionados:
Autor do livro: irina, lipschitz, maximal function methods sobolev spaces
Título do livro: layer layer, problem higher mathematics, problems higher mathematics, elliptic domains, boundary, lipschitz, 2063
Dados da editora
Autor: Irina Mitrea; Marius Mitrea
Título: Lecture Notes in Mathematics; Multi-Layer Potentials and Boundary Problems - for Higher-Order Elliptic Systems in Lipschitz Domains
Editora: Springer; Springer Berlin
424 Páginas
Ano de publicação: 2013-01-05
Berlin; Heidelberg; DE
Impresso / Feito em
Língua: Inglês
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
POD
X, 424 p.
BC; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Mathematik; 35C15, 78A30, 78A45, 31B10, 35J05, 35J25; Lipschitz domains; Whitney arrays; multiple layers; trace and extensions; partial differential equations; Potential Theory; Differential Equations; Integral Equations; Fourier Analysis; Differentialrechnung und -gleichungen; Integralrechnung und -gleichungen; Funktionalanalysis und Abwandlungen; EA
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.Aimed at people working in different areas of mathematics with different levels of expertise, and with different goals in mind The topics are new and mathematically sophisticated Readable, self-contained and has pedagogical value Comprehensive range of topics makes a suitable and much needed reference for mathematicians and engineers Includes supplementary material: sn.pub/extras
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