Harnack inequality and regularity for degenerate quasilinear elliptic equations. (English) Zbl 1186.35083
Summary: 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.
MSC:
| 35J70 | Degenerate elliptic equations |
| 35J62 | Quasilinear elliptic equations |
| 35B45 | A priori estimates in context of PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35D30 | Weak solutions to PDEs |
Keywords:
Harnack inequality; strong \(A_{\infty}\) weights; degenerate elliptic equations; Stummel class; Morrey spacesReferences:
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