Multi-Layer Potentials and Boundary Problems: for Higher-Order Elliptic Systems in Lipschitz Domains

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Irina Mitrea Marius Mitrea

Multi-Layer Potentials and Boundary Problems

for Higher-Order Elliptic Systems in Lipschitz Domains

Irina Mitrea, Marius Mitrea

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
05 January 2013

Functional analysis & transforms; Differential calculus & equations; Integral calculus & equations; Stochastics

Series: Lecture Notes in Mathematics

Summary
Details

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.

By: Irina Mitrea, Marius Mitrea
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: 2013 ed.
Volume: 2063
Dimensions: Height: 235mm, Width: 155mm, Spine: 22mm
Weight: 6.555kg
ISBN: 9783642326653
ISBN 10: 364232665X
Series: Lecture Notes in Mathematics
Pages: 424
Publication Date: 05 January 2013
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active