Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains by Mikhail BorsukTransmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains by Mikhail Borsuk

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

byMikhail Borsuk

Paperback | August 20, 2010

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The goal of this book is to investigate the behavior of weak solutions to the elliptictransmisssion problem in a neighborhood of boundary singularities: angular and conicpoints or edges. We consider this problem both for linear and quasilinear (till now very littlestudied) equations. All results are given with complete proofs. A principal new feature of our work is the consideration of our estimates of weak solutionsto the transmission problem for linear elliptic equations with minimal smooth coecients in ndimensional conic domains. Only few works are devoted to the transmission problem for quasilinear elliptic equations. Therefore, we investigate the weak solutions for general divergence quasilinear elliptic second-order equations in n-dimensional conic domains or in domains with edges. The basis of our research is the metod of integrodifferential inequalities. Such inequalities withexact estimating constants allow to establish possible or best possible estimates of solutionsto boundary value problems for elliptic equations near singularities on the boundary. We provenew Friedrichs - Wirtinger type inequality and apply it to the investigation of the behavior ofweak solutions to the transmission problem.The book will be of interest to specialists in elliptic boundary value problems and applications as well as to graduate students.
Title:Transmission Problems for Elliptic Second-Order Equations in Non-Smooth DomainsFormat:PaperbackDimensions:220 pagesPublished:August 20, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034604769

ISBN - 13:9783034604765

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Table of Contents

Preface.- Introduction.- 1 Preliminaries.- 2 Eigenvalue problem and integro-differential inequalities.- 3 Best possible estimates of solutions to the transmission problem for linear elliptic divergence second order equations in a conical domain.- 4 Transmission problem for the Laplace operator with N different media.- 5 Transmission problem for weak quasi-linear elliptic equations in a conical domain.- 6 Transmission problem for strong quasi-linear elliptic equations in a conical domain.- 7 Best possible estimates of solutions to the transmission problem for a quasi-linear elliptic divergence second order equation in a domain with a boundary edge.- Bibliography.- Index.- Notation Index.