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Titlebook: Sobolev Spaces in Mathematics II; Applications in Anal Vladimir Maz‘ya Book 2009 Springer-Verlag New York 2009 Boundary value problem.Poten

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书目名称Sobolev Spaces in Mathematics II
副标题Applications in Anal
编辑Vladimir Maz‘ya
视频video
概述Presentation of new results on the latest topics of the theory Sobolev spaces, partial differential equations, analysis and mathematical physics.The authors and editors are world-known specialists, wo
丛书名称International Mathematical Series
图书封面Titlebook: Sobolev Spaces in Mathematics II; Applications in Anal Vladimir Maz‘ya Book 2009 Springer-Verlag New York 2009 Boundary value problem.Poten
描述.Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. ..Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included..
出版日期Book 2009
关键词Boundary value problem; Potential; Sobolev space; analysis; mathematical physics; partial differential eq
版次1
doihttps://doi.org/10.1007/978-0-387-85650-6
isbn_softcover978-1-4419-2758-3
isbn_ebook978-0-387-85650-6Series ISSN 1571-5485 Series E-ISSN 1574-8944
issn_series 1571-5485
copyrightSpringer-Verlag New York 2009
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Sobolev Spaces and their Relatives: Local Polynomial Approximation Approach,ons. The study includes such topics as embeddings and extensions, pointwise differentiability and Luzin type theorems, nonlinear approximation by piecewise polynomials and splines, and the real interpolation.
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Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains,iodic) outlets to infinity. The structure of the spectra is studied for operators generated by the corresponding sesquilinear forms. In addition to general results, approaches and methods are discussed to get a piece of infor mation on continuous, point, and discrete spectra, in particular, for specific problems in the mathematical physics.
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Sobolev in Siberia,Reminiscence. Supplied with photos.
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Estimates for Completely Integrable Systems of Differential Operators and Applications,A criterion for the complete integrability of some class of systems of differential equations is established. In the proof, the corresponding system for a matrix-valued function Z of class ..(Ω) is used. Applications to differential geometry (in particular, the stability in the Bonnet theorem) are discussed.
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,Counting Schrödinger Boundstates: Semiclassics and Beyond,This is a survey of the basic results on the behavior of the num ber of the eigenvalues of a Schrödinger operator, lying below its essential spectrum. We discuss both fast decaying potentials, for which this behavior is semiclassical, and slowly decaying potentials, for which the semiclassical rules are violated.
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