Harnack inequality and regularity for degenerate quasilinear elliptic equations

Details Harnack inequality and regularity for degenerate quasilinear elliptic equations Harnack inequality and regularity for degenerate quasilinear elliptic equations

2010-10-02

arxiv.org/abs/1010.0322v1

Mathematische Zeitschrift, 264/3, 679-695 (2010)

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00209-009-0485-z

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form.

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