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On the continuity of minimizers for quasilinear functionals |
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| Authors: | David Cruz-Uribe Patrizia Di Gironimo Luigi D’Onofrio |
| Institution: | 1. SFO, Dept. of Mathematics, Trinity College, Hartford, CT, 06106-3100, USA 2. Dipartimento di Matematica e Informatica, Università degli Studi di Salerno Via Ponte don Melillo, 84084, Fisciano (SA), Italy 4. Salerno, Italy 3. Dipartimento di Statistica e Matematica per la Ricerca Economica, Università “Parthenope”, Via Medina 40, 80131, Napoli, Italy |
| 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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