Memoirs of the American Mathematical Society 2013; 106 pp; softcover Volume: 223 ISBN10: 0821887408 ISBN13: 9780821887400 List Price: US$72 Individual Members: US$43.20 Institutional Members: US$57.60 Order Code: MEMO/223/1051
 In this monograph the author investigates divergenceform elliptic partial differential equations in twodimensional 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 \(L^q\) can be solved for \(q<\infty\) large enough. He also shows that the Neumann and regularity problems with boundary data in \(L^p\) can be solved for \(p>1\) small enough, and provide an endpoint result at \(p=1\). 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
