Logo - springer
Slogan - springer

Mathematics - Analysis | Multi-Layer Potentials and Boundary Problems - for Higher-Order Elliptic Systems in Lipschitz

Multi-Layer Potentials and Boundary Problems

for Higher-Order Elliptic Systems in Lipschitz Domains

Series: Lecture Notes in Mathematics, Vol. 2063

Mitrea, Irina, Mitrea, Marius

2013, X, 424 p.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-3-642-32666-0

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase

learn more about Springer eBooks

add to marked items


Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-3-642-32665-3

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

  • 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

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.

Content Level » Research

Keywords » 35C15, 78A30, 78A45, 31B10, 35J05, 35J25 - Lipschitz domains - Whitney arrays - multiple layers - trace and extensions

Related subjects » Analysis - Dynamical Systems & Differential Equations

Table of contents / Preface / Sample pages 

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Potential Theory.