A Uniform Boundedness Result for Solutions to the Liouville Type Equation with Boundary Singularity

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A Uniform Boundedness Result for Solutions to the Liouville Type Equation with Boundary Singularity

J. Math. Sci. Univ. Tokyo
Vol. 23 (2016), No. 2, Page 487--497.

Bahoura, Samy Skander
A Uniform Boundedness Result for Solutions to the Liouville Type Equation with Boundary Singularity
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
We give blow-up behavior of a sequence of solutions of a Liouville-type problem with a singular weight and Dirichlet boundary conditions. As an application we derive a compactness criterion in the same spirit of the well known Brezis-Merle's result.

Keywords: Blow-up, boundary, singularity, a priori estimate, Lipschitz condition.

Mathematics Subject Classification (2010): 35J60, 35B44, 35B45.

Mathematical Reviews Number: MR3469006

Received: 2014-03-18

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