The extremal solution of a boundary reaction problem
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Abstract
We consider
Delta u = 0 in Omega, partial derivative u/partial derivative v = lambda f(u) on Gamma(1), u= 0 on Gamma(2)
where lambda > 0, f(u) = e(u) or f(u) = (1 + u)(p), Gamma(1), Gamma(2) is a partition of partial derivative Omega and Omega subset of R-N. We determine sharp conditions on the dimension N and p > 1 such that the extremal solution is bounded, where the extremal solution refers to the one associated to the largest lambda for which a solution exists.
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COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 7 Issue: 4 Pages: 795-817 Published: JUL 2008
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