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Semilinear elliptic equations with uniform blow-up on the boundary

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Abstract

We prove the existence and the uniqueness of a solutionu of−Lu+h|u| α-1u=f in some open domain ℝd, whereL is a strongly elliptic operator,f a nonnegative function, and α>1, under the assumption that ∂G is aC 2 compact hypersurface, lim x→∂G (dist(x, ∂G))2α/(α-1) f(x)=0, and lim x→∂G u(x)=∞.

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  1. Département de Mathématiques Faculté Des Sciences, Universite De Tours, Parc De Grandmont, F 37200, Tours, France

    Laurent Veron

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  1. Laurent Veron
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Veron, L. Semilinear elliptic equations with uniform blow-up on the boundary. J. Anal. Math. 59, 231–250 (1992). https://doi.org/10.1007/BF02790229

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  • DOI: https://doi.org/10.1007/BF02790229

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