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  • Book
  • © 2013

Multi-Layer Potentials and Boundary Problems

for Higher-Order Elliptic Systems in Lipschitz Domains

  • Aimed at people working in different areas of mathematics with different levels of expertise, and with different goals in mind

  • The topics are new and mathematically sophisticated Readable, self-contained and has pedagogical value

  • Comprehensive range of topics makes a suitable and much needed reference for mathematicians and engineers

  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2063)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
  2. Introduction

    • Irina Mitrea, Marius Mitrea
    Pages 1-19
  3. Function Spaces of Whitney Arrays

    • Irina Mitrea, Marius Mitrea
    Pages 125-197
  4. The Double Multi-Layer Potential Operator

    • Irina Mitrea, Marius Mitrea
    Pages 199-252
  5. The Single Multi-Layer Potential Operator

    • Irina Mitrea, Marius Mitrea
    Pages 253-291
  6. Back Matter

    Pages 405-424

About this book

Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Calderón, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatment based on this approach.

This research monograph lays, for the first time, the mathematical foundation aimed at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including layer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions, boundary value problems with data in Whitney–Lebesque spaces, Whitney–Besov spaces, Whitney–Sobolev- based Lebesgue spaces, Whitney–Triebel–Lizorkin spaces,Whitney–Sobolev-based Hardy spaces, Whitney–BMO and Whitney–VMO spaces.

Keywords

  • 35C15, 78A30, 78A45, 31B10, 35J05, 35J25
  • Lipschitz domains
  • Whitney arrays
  • multiple layers
  • trace and extensions
  • partial differential equations

Authors and Affiliations

  • Department of Mathematics, Temple University, Philadelphia, USA

    Irina Mitrea

  • , Department of Mathematics, University of Missouri, Columbia, USA

    Marius Mitrea

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions