Oblique Derivative Problems For Elliptic Equations (eBook)
by GARY M LIEBERMAN (Author)

 87,648 Words
 528 Pages
This book gives an uptodate 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 Estimates
 Classical Schauder Theory from a Modern Perspective
 The Miller Barrier and Some Supersolutions for Oblique Derivative Problems
 Hölder Estimates for First and Second Derivatives
 Weak Solutions
 Strong Solutions
 Viscosity Solutions of Oblique Derivative Problems
 Pointwise Bounds for Solutions of Problems with Quasilinear Equations
 Gradient Estimates for General Form Oblique Derivative Problems
 Gradient Estimates for the Conormal Derivative Problems
 Higher Order Estimates and Existence of Solutions for Quasilinear Oblique Derivative Problems
 Oblique Derivative Problems for Fully Nonlinear Elliptic Equations
Readership: For the professional researcher in mathematics.
 Released: March 26, 2013
 Categories: Education, Science & Nature
 Language: English
 Publisher: World Scientific Publishing Company
 ISBN10: 9814452343
 ISBN13: 9789814452342