Calculus of Variations and Geometric Measure Theory

G. Di Fazio - Maria Stella Fanciullo - P. Zamboni

Harnack inequality and regularity for degenerate quasilinear elliptic equations

created by difazio on 05 Oct 2021



Inserted: 5 oct 2021

Year: 2010

ArXiv: 1010.0322 PDF


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.