We extend the p-harmonic approximation lemma proved by Duzaar and Mingione for p-harmonic functions to phi-harmonic functions, where phi is a convex function. The proof is direct and is based on the Lipschitz truncation technique. We apply the approximation lemma to prove Holder continuity for the gradient of a solution of a phi-harmonic system with critical growth.
THE PHI-HARMONIC APPROXIMATION AND THE REGULARITY OFPHI-HARMONIC MAPS / L., Diening; Stroffolini, Bianca; Verde, Anna. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 253:(2012), pp. 1943-1958. [10.1016/j.jde.2012.06.010]
THE PHI-HARMONIC APPROXIMATION AND THE REGULARITY OFPHI-HARMONIC MAPS
STROFFOLINI, BIANCA
;VERDE, ANNA
2012
Abstract
We extend the p-harmonic approximation lemma proved by Duzaar and Mingione for p-harmonic functions to phi-harmonic functions, where phi is a convex function. The proof is direct and is based on the Lipschitz truncation technique. We apply the approximation lemma to prove Holder continuity for the gradient of a solution of a phi-harmonic system with critical growth.File in questo prodotto:
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