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Elliptic Problems in Nonsmooth DomainsElliptic Problems in Nonsmooth Domains

Pierre Grisvard

Classics in Applied Mathematics 69

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.

This book is intended for researchers and graduate students in computational science and numerical analysis who work with theoretical and numerical PDEs. Readers need only a background in functional analysis to find the material accessible.

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 Hölder Functions;
Chapter 7: A Model Fourth-Order Problem;
Chapter 8: Miscellaneous;

About the Authors

Pierre Grisvard (1940-1994) was Professor of Mathematics at the University of Nice, France, and Director of the Institute Henri Poincaré in Paris.

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2011 / xiv + 410 / Softcover / ISBN 978-1-611972-02-3
List Price $99.00 / SIAM Member Price $69.30 / Order Code CL69
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