Geodesic
On the continuity of minimizers for quasilinear functionals
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 111-116
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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.
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.
DOI : 10.1007/s10587-012-0020-y
Classification : 49J10, 49N60
Keywords: regularity; quasilinear functionals; calculus of variations 
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Cruz-Uribe, David; Di Gironimo, Patrizia; D'Onofrio, Luigi. On the continuity of minimizers for quasilinear functionals. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 111-116. doi: 10.1007/s10587-012-0020-y

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