Local Lipschitz regularity for degenerate elliptic systems

  • Frank Duzaar

    Department Mathematik, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, 91054 Erlangen, Germany
  • Giuseppe Mingione

    Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/a, Campus, 43100 Parma, Italy


We start presenting an -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.

Cite this article

Frank Duzaar, Giuseppe Mingione, Local Lipschitz regularity for degenerate elliptic systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 6, pp. 1361–1396

DOI 10.1016/J.ANIHPC.2010.07.002