Elliptic partial differential equations with almost-real coefficients
Author(s)
Bibliographic Information
Elliptic partial differential equations with almost-real coefficients
（Memoirs of the American Mathematical Society, no. 1051）
American Mathematical Society, c2012
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Note
"May 2013, volume 223, number 1051 (fifth of 5 numbers)."
Includes bibliographical references (p. 105-108)
Description and Table of Contents
Description
In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates.
He shows that for such operators, the Dirichlet problem with boundary data in Lq can be solved for q<∞ large enough. He also shows that the Neumann and regularity problems with boundary data in Lp can be solved for p>1 small enough, and provide an endpoint result at p=1.
Table of Contents
Table of Contents
Introduction
Definitions and the main theorem
Useful theorems
The Fundamental solution
Properties of layer potentials
Boundedness of layer potentials
Invertibility of layer potentials and other properties
Uniqueness of solutions
Boundary data in $H^1(\partial V)$
Concluding remarks
Bibliography
by "Nielsen BookData"