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Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains
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Catalogue Information
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
Links to Related Works
Subject References:
Differential equations, Partial
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Mathematics
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Partial differential equations
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Authors:
Borsuk, Mikhail
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Corporate Authors:
SpringerLink (Online service)
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Series:
Frontiers in Mathematics
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Classification:
515.353
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515.353 (DDC 23)
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