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

Local Lipschitz regularity for degenerate elliptic systems

created by mingione on 30 Sep 2012


Published Paper

Inserted: 30 sep 2012
Last Updated: 30 sep 2012

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 27
Pages: 1361-1396
Year: 2010


We start presenting an $L^{\infty}$-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


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