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

  • Book
  • © 2010

Overview

Authors:
  1. Mikhail Borsuk

    1. Dept. Mathematics & Informatics, University of Warmia & Mazury, Olsztyn, Poland

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  • Estimates of weak solutions to the transmission problem for linear elliptic equations with minimal smooth coefficients in n-dimensional conic domains
  • Investigation of weak solutions for general divergence quasi-linear elliptic second-order equations in n-dimensional conic domains or in domains with edges
  • Includes supplementary material: sn.pub/extras

Part of the book series: Frontiers in Mathematics (FM)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    • Mikhail Borsuk
    Pages 1-4

  3. Preliminaries

    • Mikhail Borsuk
    Pages 5-15

  4. Eigenvalue problem and integro-differential inequalities

    • Mikhail Borsuk
    Pages 17-32

  5. Best possible estimates of solutions to the transmission problem for linear elliptic divergence second-order equations in a conical domain

    • Mikhail Borsuk
    Pages 33-66

  6. Transmission problem for the Laplace operator with N different media

    • Mikhail Borsuk
    Pages 67-103

  7. Transmission problem for weak quasi-linear elliptic equations in a conical domain

    • Mikhail Borsuk
    Pages 105-133

  8. Transmission problem for strong quasi-linear elliptic equations in a conical domain

    • Mikhail Borsuk
    Pages 135-169

  9. 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

    • Mikhail Borsuk
    Pages 171-207

  10. Back Matter

    Pages 209-220
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Keywords

About this book

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.

Authors and Affiliations

  • Dept. Mathematics & Informatics, University of Warmia & Mazury, Olsztyn, Poland

    Mikhail Borsuk

Bibliographic Information

  • Book Title: Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

  • Authors: Mikhail Borsuk

  • Series Title: Frontiers in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0346-0477-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2010

  • Softcover ISBN: 978-3-0346-0476-5Published: 20 August 2010

  • eBook ISBN: 978-3-0346-0477-2Published: 02 September 2010

  • Series ISSN: 1660-8046

  • Series E-ISSN: 1660-8054

  • Edition Number: 1

  • Number of Pages: XII, 220

  • Number of Illustrations: 1 illustrations in colour

  • Topics: Partial Differential Equations

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