4,068 research outputs found

    Harnack inequality for fractional sub-Laplacians in Carnot groups

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    In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a technique recently introduced by Caffarelli and Silvestre. In addition, we write explicitly the Poisson kernel for a class of degenerate subelliptic equations in product-type Carnot groups

    Harnack inequality and regularity for degenerate quasilinear elliptic equations

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    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∞A_\infty weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove C1,αC^{1,\alpha} local estimates for solutions of a degenerate equation in non divergence form
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