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A sup+inf inequality for Liouville type equations with weights

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Abstract

We generalize a result by H. Brezis, Y. Y. Li and I. Shafrir [6] and obtain an Harnack type inequality for solutions of −Δu = |x|2α Ve u in Ω for Ω ⊂ ℝ2 open, α ∈ (−1, 0) and V any Lipschitz continuous function satisfying 0 < a ≤ V ≤ b < ∞ and ‖∇V‖∞ ≤ A.

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Authors and Affiliations

  1. Department of Mathematics, University of Rome “tor Vergata”, Via Della Ricerca Scientifica N.1, 00133, Roma, Italy

    Daniele Bartolucci

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  1. Daniele Bartolucci
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Correspondence to Daniele Bartolucci.

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Research partially supported by FIRB-IDEAS project “Analysis and beyond”.

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Bartolucci, D. A sup+inf inequality for Liouville type equations with weights. JAMA 117, 29–46 (2012). https://doi.org/10.1007/s11854-012-0013-7

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  • DOI: https://doi.org/10.1007/s11854-012-0013-7

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