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Riesz potential estimates for a general class of quasilinear equations

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Abstract

We consider solutions to nonlinear elliptic equations with measure data and general growth and ellipticity conditions of degenerate type, as considered in Lieberman (Commun Partial Differ Equ 16:311–361, 1991); 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.

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Acknowledgments

This research has been supported by the ERC Grant 207573 “Vectorial Problems”.

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  1. Department of Mathematics, Uppsala University, Lägerhyddsvägen 1, SE-751 06, Uppsala, Sweden

    Paolo Baroni

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  1. Paolo Baroni
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Correspondence to Paolo Baroni.

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Communicated by A. Chang.

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Baroni, P. Riesz potential estimates for a general class of quasilinear equations. Calc. Var. 53, 803–846 (2015). https://doi.org/10.1007/s00526-014-0768-z

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  • DOI: https://doi.org/10.1007/s00526-014-0768-z

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