Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains
Series: Frontiers in Mathematics;
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Product details:
- Edition number 2010
- Publisher Birkhäuser
- Date of Publication 20 August 2010
- Number of Volumes 1 pieces, Book
- ISBN 9783034604765
- Binding Paperback
- No. of pages220 pages
- Size 240x170 mm
- Weight 442 g
- Language English
- Illustrations 1 Illustrations, color 0
Categories
Short description:
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 Friedrichs?Wirtinger 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.
Long description:
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 Friedrichs-Wirtinger 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.
MoreTable of Contents:
Preliminaries.- Eigenvalue problem and integro-differential inequalities.- Best possible estimates of solutions to the transmission problem for linear elliptic divergence second-order equations in a conical domain.- Transmission problem for the Laplace operator with N different media.- Transmission problem for weak quasi-linear elliptic equations in a conical domain.- Transmission problem for strong quasi-linear elliptic equations in a conical domain.- 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.
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