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

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains
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Field name Details
Dewey Class 515.353
Title Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains ([Ebook]) / by Mikhail Borsuk.
Author Borsuk, Mikhail
Other name(s) SpringerLink (Online service)
Publication Basel : Springer Basel , 2010.
Physical Details XI, 218 pages: 1 illus. in color. : online resource.
Series Frontiers in Mathematics 1660-8046
ISBN 9783034604772
Summary Note The goal of this book is to investigate the behavior of weak solutions of the elliptic transmission problem in a neighborhood of boundary singularities: angular and conic points or edges. This problem is discussed for both linear and quasilinear equations. A principal new feature of this book is the consideration of our estimates of weak solutions of the transmission problem for linear elliptic equations with minimal smooth coeciffients in n-dimensional 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 the present work is the method of integro-differential inequalities. Such inequalities with exact estimating constants allow us to establish possible or best possible estimates of solutions to boundary value problems for elliptic equations near singularities on the boundary. A new FriedrichsâWirtinger type inequality is proved and applied to the investigation of the behavior of weak solutions of the transmission problem. All results are given with complete proofs. The book will be of interest to graduate students and specialists in elliptic boundary value problems and applications.:
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-3-0346-0477-2
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