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Boundary regularity for linear and quasilinear variational inequalities

Published online by Cambridge University Press:  14 November 2011

Gary M. Lieberman
Gary M. Lieberman
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.
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Synopsis

A method of Jensen is extended to show that the second derivatives of the solutions of various linear obstacle problems are bounded under weaker regularity hypotheses on the dataof the problem than were allowed by Jensen. They are, in fact, weak enough that the linear results imply the boundedness of the second derivatives for quasilinear problems as well. Comparisons are made with previously known results, some of which are proved by similar methods. Both Dirichlet and oblique derivative boundary conditions are considered. Corresponding results for parabolic obstacle problems are proved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 319 - 326
Copyright
Copyright © Royal Society of Edinburgh 1989

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