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View CartElliptic Problems in Nonsmooth Domains
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Description
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.
Keywords: nonsmooth, Sobolev spaces, ellipses, boundary value problems, singularities
Table of Contents
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Front Matter
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1. Sobolev Spaces
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5. More Singular Solutions
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7. A Model Fourth-Order Problem
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8. Miscellaneous
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Back Matter
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Excerpt
Since the publication of Pierre Grisvard's monograph in 1985, the theory of elliptic problems in nonsmooth domains has become increasingly important for research in partial differential equations and their numerical solutions. While significant advances have occurred during the last two decades, Grisvard's monograph remains an excellent introduction to the subject and a good source for the basic material.
©2011 SIAM
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