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On the continuity of minimizers for quasilinear functionals

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Abstract

In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by log log(1/|x|)−1. Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 6 (2007), 103–116.

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Authors and Affiliations

  1. Salerno, Italy

    Patrizia Di Gironimo

  2. SFO, Dept. of Mathematics, Trinity College, Hartford, CT, 06106-3100, USA

    David Cruz-Uribe

  3. Dipartimento di Matematica e Informatica, Università degli Studi di Salerno Via Ponte don Melillo, 84084, Fisciano (SA), Italy

    Patrizia Di Gironimo

  4. Dipartimento di Statistica e Matematica per la Ricerca Economica, Università “Parthenope”, Via Medina 40, 80131, Napoli, Italy

    Luigi D’Onofrio

Authors
  1. David Cruz-Uribe
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  2. Patrizia Di Gironimo
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  3. Luigi D’Onofrio
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Correspondence to David Cruz-Uribe.

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Cruz-Uribe, D., Di Gironimo, P. & D’Onofrio, L. On the continuity of minimizers for quasilinear functionals. Czech Math J 62, 111–116 (2012). https://doi.org/10.1007/s10587-012-0020-y

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  • DOI: https://doi.org/10.1007/s10587-012-0020-y

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