Oblique Derivative Problems for Elliptic Equations

Gary M. Lieberman

This book gives an up-to-date exposition on the theory of oblique derivative problems for elliptic equations. The modern analysis of shock reflection was made possible by the theory of oblique derivative problems developed by the author. Such problems also arise in many other physical situations such as the shape of a capillary surface and problems of optimal transportation. We begin with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. A final chapter discusses some of the applications. In addition, notes to each chapter give a history of the topics in that chapter and suggestions for further reading.