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Regularity of an elliptic problem with a singular nonlinearity

Published online by Cambridge University Press:  14 November 2011

Changfeng Gui
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012, U.S.A.
Fang Hua Lin
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012, U.S.A.

Synopsis

We study a semilinear boundary value problem with the feature that the vanishing boundary value makes the equation singular. We prove that the positive solution is in general Hölder-continuous up to the boundary and has even better regularity in some special cases.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1993

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