Lecture Notes in Mathematics

Multi-Layer Potentials and Boundary Problems

for Higher-Order Elliptic Systems in Lipschitz Domains

Authors: Mitrea, Irina, Mitrea, Marius

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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.

Table of contents (6 chapters)

  • Introduction

    Mitrea, Irina (et al.)

    Pages 1-19

  • Smoothness Scales and Calderón–Zygmund Theory in the Scalar–Valued Case

    Mitrea, Irina (et al.)

    Pages 21-124

  • Function Spaces of Whitney Arrays

    Mitrea, Irina (et al.)

    Pages 125-197

  • The Double Multi-Layer Potential Operator

    Mitrea, Irina (et al.)

    Pages 199-252

  • The Single Multi-Layer Potential Operator

    Mitrea, Irina (et al.)

    Pages 253-291

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-642-32666-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.95
price for USA
  • ISBN 978-3-642-32665-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Multi-Layer Potentials and Boundary Problems
Book Subtitle
for Higher-Order Elliptic Systems in Lipschitz Domains
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2063
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-32666-0
DOI
10.1007/978-3-642-32666-0
Softcover ISBN
978-3-642-32665-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 424
Topics