Oblique Derivative Problems For Elliptic Equations

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. The author begins the book with basic results for linear oblique derivative problems and work through the theory for quasilinear and nonlinear problems. The 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.
Contents:Pointwise EstimatesClassical Schauder Theory from a Modern PerspectiveThe Miller Barrier and Some Supersolutions for Oblique Derivative ProblemsHölder Estimates for First and Second DerivativesWeak SolutionsStrong SolutionsViscosity Solutions of Oblique Derivative ProblemsPointwise Bounds for Solutions of Problems with Quasilinear EquationsGradient Estimates for General Form Oblique Derivative ProblemsGradient Estimates for the Conormal Derivative ProblemsHigher Order Estimates and Existence of Solutions for Quasilinear Oblique Derivative ProblemsOblique Derivative Problems for Fully Nonlinear Elliptic Equations
Readership: For the professional researcher in mathematics.