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arXiv · 1809.05684

Uniform bounds for solutions to elliptic problems on simply connected planar domains

Luca Battaglia
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Abstract

We consider the singular Liouville equation and the Henon-Lane-Emden problem on simply connected planar domains. We show that any solution to each problem must satisfy a uniform bound on the mass. The same results applies to some systems and more general non-linearities. The proofs are based on the Riemann mapping theorem and a Pohozaev-type identity.

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Luca Battaglia. 2018-09-15. Uniform bounds for solutions to elliptic problems on simply connected planar domains. https://arxiv.org/abs/1809.05684

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