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On a Poincaré type formula for solutions of singular and degenerate elliptic equations

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Abstract

We provide a geometric Poincaré type formula for stable solutions of −Δ p (u) = f(u). From this, we derive a symmetry result in the plane. This work is a refinement of previous results obtained by the authors under further integrability and regularity assumptions.

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Authors and Affiliations

  1. LAMFA, Faculté de Mathématiques et d’Informatique, Université de Picardie Jules Verne, CNRS UMR 6140, 33, rue Saint-Leu, 80039, Amiens Cedex 1, France

    Alberto Farina

  2. Dipartimento di Matematica, Università della Calabria, Ponte Pietro Bucci, 31 B, 87036, Arcavacata di Rende, Cosenza, Italy

    Berardino Sciunzi

  3. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della ricerca scientifica, 00133, Rome, Italy

    Enrico Valdinoci

Authors
  1. Alberto Farina
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  2. Berardino Sciunzi
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  3. Enrico Valdinoci
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Corresponding author

Correspondence to Enrico Valdinoci.

Additional information

Enrico Valdinoci is supported by FIRB “Analysis and Beyond” and GNAMPA “Equazioni nonlineari su varietà: proprietà qualitative e classificazione delle soluzioni”.

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Farina, A., Sciunzi, B. & Valdinoci, E. On a Poincaré type formula for solutions of singular and degenerate elliptic equations. manuscripta math. 132, 335–342 (2010). https://doi.org/10.1007/s00229-010-0349-1

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  • DOI: https://doi.org/10.1007/s00229-010-0349-1

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