Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 567-577

HÖLDER CONTINUITY OF DEGENERATE p-HARMONIC FUNCTIONS

Flavia Giannetti and Antonia Passarelli di Napoli

Università di Napoli "Federico II", Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
via Cintia - 80126 Napoli, Italia; giannett 'at' unina.it

Università di Napoli "Federico II", Dipartimento di Matematica e Applicazioni "R. Caccioppoli"
via Cintia - 80126 Napoli, Italia; antonia.passarelli 'at' unina.it

Abstract. We prove a partial Hölder continuity result for finite energy solutions of degenerate elliptic equations. The function that measures the degeneracy of the problem is assumed to belong to a suitable Sobolev class. Moreover, we prove an analogous result for infinite energy solutions provided their gradients have a suitable degree of integrability.

2010 Mathematics Subject Classification: Primary 35B65, 31B05.

Key words: Degenerate elliptic equations, Hölder's continuity.

Reference to this article: F. Giannetti and A. Passarelli di Napoli: Hölder continuity of degenerate p-harmonic functions. Ann. Acad. Sci. Fenn. Math. 39 (2014), 567-577.

Full document as PDF file

doi:10.5186/aasfm.2014.3949