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A ‘sup + C inf’ inequality for the equation –Δu = V eu|x|2α

Published online by Cambridge University Press:  08 December 2010

Daniele Bartolucci
Daniele Bartolucci
Affiliation:
Department of Mathematics, University of Rome ‘Tor Vergata’, Via della Ricerca Scientifica n.1, 00133 Roma, Italy
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Abstract

We generalize the ‘sup+C inf’ inequality obtained by Shafrir to the solutions of

with Ω ⊂ ℝ2 open and bounded, α ∈ (0,1) and V any measurable function which satisfies 0 < a ≤ V ≤ b < + ∞.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 6 , December 2010 , pp. 1119 - 1139
Copyright
Copyright © Royal Society of Edinburgh 2010

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