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A global estimate for the gradient in a singular elliptic boundary value problem

Published online by Cambridge University Press:  14 November 2011

Manuel A. del Pino
Manuel A. del Pino
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
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Synopsis

We investigate the singular problem

where Ω is a bounded smooth domain, k a bounded, nonnegative measurable function and v Ω 0. For the solution u to this problem, which is shown to exist if k(x) > 0 on some subset of Ω with positive measure, a uniform bound for |∇u| in Ω is derived when k(x) ≧ ψ (dist (x, ∂Ω)) with ψ (s)/sv ∈ Lp(0, a) for some a > 0, p > 1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 122 , Issue 3-4 , 1992 , pp. 341 - 352
Copyright
Copyright © Royal Society of Edinburgh 1992

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