A global estimate for the gradient in a singular elliptic boundary value problem
- 1 January 1992
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 122 (3-4) , 341-352
Abstract
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.Keywords
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