Gradient estimates via linear and nonlinear potentials

Duzaar F, Mingione G (2010)

Publication Type: Journal article

Publication year: 2010

Journal

Journal of Functional Analysis Elsevier

Publisher: Elsevier

Book Volume: 259

Pages Range: 2961-2998

Journal Issue: 11

DOI: 10.1016/j.jfa.2010.08.006

Abstract

We prove new potential and nonlinear potential pointwise gradient estimates for solutions to measure data problems, involving possibly degenerate quasilinear operators whose prototype is given by -Δpu=μ. In particular, no matter the nonlinearity of the equations considered, we show that in the case p≤2 a pointwise gradient estimate is possible using standard, linear Riesz potentials. The proof is based on the identification of a natural quantity that on one hand respects the natural scaling of the problem, and on the other allows to encode the weaker coercivity properties of the operators considered, in the case p≤2. In the case p>2 we prove a new gradient estimate employing nonlinear potentials of Wolff type.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

University of Parma / Università degli Studi di Parma IT Italy (IT)

How to cite

APA:

Duzaar, F., & Mingione, G. (2010). Gradient estimates via linear and nonlinear potentials. Journal of Functional Analysis, 259(11), 2961-2998. https://doi.org/10.1016/j.jfa.2010.08.006

MLA:

Duzaar, Frank, and Giuseppe Mingione. "Gradient estimates via linear and nonlinear potentials." Journal of Functional Analysis 259.11 (2010): 2961-2998.

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