Local Lipschitz regularity for degenerate elliptic systems
Frank Duzaar, Giuseppe Mingione · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 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.