Geodesic
Local Lipschitz regularity for degenerate elliptic systems
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 6, pp. 1361-1396

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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.

@article{AIHPC_2010__27_6_1361_0,
     author = {Duzaar, Frank and Mingione, Giuseppe},
     title = {Local {Lipschitz} regularity for degenerate elliptic systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1361--1396},
     publisher = {Elsevier},
     volume = {27},
     number = {6},
     year = {2010},
     doi = {10.1016/j.anihpc.2010.07.002},
     mrnumber = {2738325},
     zbl = {1216.35063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2010.07.002/}
}
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Duzaar, Frank; Mingione, Giuseppe. Local Lipschitz regularity for degenerate elliptic systems. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 6, pp. 1361-1396. doi: 10.1016/j.anihpc.2010.07.002

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