Gradient estimates via non-linear potentials

2009/06/26 by Duzaar, Frank, Mingione, Giuseppe · 5 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0906.4939

Abstract

We present pointwise gradient bounds for solutions to p-Laplacean type non-homogeneous equations employing non-linear Wolff type potentials, and then prove similar bounds, via suitable caloric potentials, for solutions to parabolic equations.

Cited by

• Local potential and Hölder estimates for the linearized Monge-Ampère equation
• Regularity for quasilinear elliptic equations in metric measure spaces
• Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces
• Gradient continuity estimates for elliptic equations of singular p-Laplace type with measure data
• Second-order boundary estimates for solutions to a class of quasilinear elliptic equations

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• Nonlinear nonlocal potential theory at the gradient level