This classic text focuses on elliptic boundary value problems in domains with nonsmooth boundaries and on problems with mixed boundary conditions. Its contents are essential for an understanding of the behavior of numerical methods for partial differential equations (PDEs) on two-dimensional domains with corners. Elliptic Problems in Nonsmooth Domains provides a careful and self-contained development of Sobolev spaces on nonsmooth domains, develops a comprehensive theory for second-order elliptic boundary value problems, and addresses fourth-order boundary value problems and numerical treatment of singularities.
* Foreword* Preface*
Chapter 1: Sobolev Spaces*
Chapter 2: Regular Second-Order Elliptic Boundary Value Problems*
Chapter 3: Second-Order Elliptic Boundary Value Problems in Convex Domains*
Chapter 4: Second-Order Boundary Value Problems in Polygons*
Chapter 5: More Singular Solutions*
Chapter 6: Results in Spaces of Holder Functions*
Chapter 7: A Model Fourth-Order Problem*
Chapter 8: Miscellaneous* Bibliography* Index.
Pierre Grisvard (1940-1994) was Professor of Mathematics at the University of Nice, France, and Director of the Institute Henri Poincare in Paris.
