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

• Main Authors: Mitrea, Irina (Author), Mitrea, Marius (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Lecture Notes in Mathematics, 2063
• Subjects: Mathematics.; Fourier analysis.; Integral equations.; Partial differential equations.; Potential theory (Mathematics).; Potential Theory.; Partial Differential Equations.; Integral Equations.; Fourier Analysis.

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...

Table of Contents:

• 1 Introduction
• 2 Smoothness scales and Caldeón-Zygmund theory in the scalar-valued case
• 3 Function spaces of Whitney arrays
• 4 The double multi-layer potential operator
• 5 The single multi-layer potential operator
• 6 Functional analytic properties of multi-layer potentials and boundary value problems.