Calculus of Variations and Geometric Measure Theory

P. Baroni

Riesz potential estimates for a general class of quasilinear equations

created by baroni on 28 May 2014
modified on 25 Aug 2014


Accepted Paper

Inserted: 28 may 2014
Last Updated: 25 aug 2014

Journal: Calc. Var. Partial Differ. Equ.
Year: 2014
Doi: 10.1007/s00526-014-0768-z


We consider solutions to nonlinear elliptic equations with measure data and general growth and ellipticity conditions as considered in Lieberman (Comm. PDE, 1991) and we prove pointwise gradient bounds for solutions in terms of linear Riesz potentials. As a direct consequence, we get optimal conditions for the continuity of the gradient.