Calculus of Variations and Geometric Measure Theory
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F. Duzaar - G. Mingione

Regularity for Degenerate Elliptic Problems via p-harmonic Approximation

created by mingione on 29 Sep 2012


Published Paper

Inserted: 29 sep 2012

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 21
Pages: 735-766
Year: 2004


We introduce a new method to prove regularity of solutions to certain degenerate elliptic problems. The method is based on the p-harmonic approximation lemma, recently proved by the authors (Calc. Var., 2004, in press), that allows to approximate functions with p-harmonic functions in the same way as the classical harmonic approximation lemma (going back to De Giorgi) does via harmonic functions. The method presented here also bypasses certain difficulties arising when treating some degenerate and singular problems with a weak structure, such as degenerate and singular quasiconvex integrals, and provides transparent and elementary proofs

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