In recent years, there has been a great deal of activity in the study of boundary value problems with minimal smoothness assumptions on the coefficients or on the boundary of the domain in question. These problems are of interest both because of their theoretical importance and the implications for applications, and they have turned out to have profound and fascinating connections with many areas of analysis. Techniques from harmonic analysis have proved to be extremely useful in these studies, both as concrete tools in establishing theorems and as models which suggest what kind of result might be true. Kenig describes these developments and connections for the study of classical boundary value problems on Lipschitz domains and for the corresponding problems for second order elliptic equations in divergence form. He also points out many interesting problems in this area which remain open.

Readership

Advanced graduate students and researchers in the fields of harmonic analysis and elliptic partial differential equations.

Reviews

"This book could be used in a course for advanced graduate students ... it is already organized in the form of a course ... will also be an excellent source book for amateurs as well as experts in this subject ... The AMS, in publishing this series, has done the mathematical community a real service by providing timely and scholarly research manuscripts at such a reasonable price."

-- Bulletin of the AMS

"The core of the work is devoted to the very recent state of the art."

-- Mathematical Reviews

Table of Contents

• Introduction
• Divergence form elliptic equations
• Some classes of examples and their perturbation theory
• Epilogue: Some further results and open problems
• References