Local Lipschitz regularity for degenerate elliptic systems

Duzaar F, Mingione G (2010)

Publication Type: Journal article

Publication year: 2010

Journal

Annales de l'Institut Henri Poincaré - Analyse Non Linéaire Elsevier Masson / Institute Henri Poincaré

Publisher: Elsevier Masson / Institute Henri Poincaré

Book Volume: 27

Pages Range: 1361-1396

DOI: 10.1016/j.anihpc.2010.07.002

Abstract

We start presenting an L∞-gradient bound for solutions to non-homogeneous p-Laplacean type systems and equations, via suitable non-linear potentials of the right-hand side. Such a bound implies a Lorentz space characterization of Lipschitz regularity of solutions which surprisingly turns out to be independent of p, and that reveals to be the same classical one for the standard Laplacean operator. In turn, the a priori estimates derived imply the existence of locally Lipschitz regular solutions to certain degenerate systems with critical growth of the type arising when considering geometric analysis problems.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

University of Parma / Università degli Studi di Parma IT Italy (IT)

How to cite

APA:

Duzaar, F., & Mingione, G. (2010). Local Lipschitz regularity for degenerate elliptic systems. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire, 27, 1361-1396. https://dx.doi.org/10.1016/j.anihpc.2010.07.002

MLA:

Duzaar, Frank, and Giuseppe Mingione. "Local Lipschitz regularity for degenerate elliptic systems." Annales de l'Institut Henri Poincaré - Analyse Non Linéaire 27 (2010): 1361-1396.

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