The $p$-harmonic approximation and the regularity of $p$-harmonic maps

Duzaar F, Mingione G (2004)

Publication Type: Journal article

Publication year: 2004

Journal

Calculus of Variations and Partial Differential Equations Springer Verlag (Germany)

Publisher: Springer Verlag (Germany)

Book Volume: 20

Pages Range: 235-256

Journal Issue: 3

URI: http://www.springerlink.com/content/97wh09at0y84v6dj/fulltext.pdf

DOI: 10.1007/s00526-003-0233-x

Abstract

We extend to the degenerate case p ≠ 2, Simon's approach to the classical regularity theory of harmonic maps of Schoen & Uhlenbeck, by proving a "p-Harmonic Approximation Lemma". This 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. Finally, we show how to combine this tool with suitable regularity estimates for solutions to degenerate elliptic systems with a critical growth right hand side, in order to obtain partial C^1,α-regularity of p-harmonic maps.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

University of Parma / Università degli Studi di Parma

Italy (IT)

How to cite

APA:

Duzaar, F., & Mingione, G. (2004). The $p$-harmonic approximation and the regularity of $p$-harmonic maps. Calculus of Variations and Partial Differential Equations, 20(3), 235-256. https://doi.org/10.1007/s00526-003-0233-x

MLA:

Duzaar, Frank, and Giuseppe Mingione. "The $p$-harmonic approximation and the regularity of $p$-harmonic maps." Calculus of Variations and Partial Differential Equations 20.3 (2004): 235-256.

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