Regularity for degenerate elliptic problems via $p$-harmonic approximation
Duzaar F, Mingione G (2004)
Publication Type: Journal article
Publication year: 2004
Journal
Publisher: Elsevier Masson / Institute Henri Poincaré
Book Volume: 21
Pages Range: 735-766
Journal Issue: 5
DOI: 10.1016/j.anihpc.2003.09.003
Abstract
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 in [F. Duzaar, G. Mingione, The p-harmonic approximation and the regularity of p-harmonic maps, 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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APA:
Duzaar, F., & Mingione, G. (2004). Regularity for degenerate elliptic problems via $p$-harmonic approximation. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 21(5), 735-766. https://dx.doi.org/10.1016/j.anihpc.2003.09.003
MLA:
Duzaar, Frank, and Giuseppe Mingione. "Regularity for degenerate elliptic problems via $p$-harmonic approximation." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 21.5 (2004): 735-766.
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