Wolff-Potential Estimates and Doubling of Subelliptic p-harmonic measures
2013 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 85, 149-159 p.Article in journal (Refereed) Published
Let be a system of C∞ vector fields in Rn satisfying Hörmander’s finite rank condition and let Ω be a non-tangentially accessible domain with respect to the Carnot–Carathéodory distance d induced by X. We prove the doubling property of certain boundary measures associated to non-negative solutions, which vanish on a portion of ∂Ω, to the equation
Given p, 1<p<∞, fixed, we impose conditions on the function A=(A1,…,Am):Rn×Rm→Rm, which imply that the equation is a quasi-linear partial differential equation of p-Laplace type structured on vector fields satisfying the classical Hörmander condition. In the case p=2 and for linear equations, our result coincides with the doubling property of associated elliptic measures. To prove our result we establish, and this is of independent interest, a Wolff potential estimate for subelliptic equations of p-Laplace type.
Place, publisher, year, edition, pages
2013. Vol. 85, 149-159 p.
IdentifiersURN: urn:nbn:se:uu:diva-186268DOI: 10.1016/j.na.2013.02.023ISI: 000318378700013OAI: oai:DiVA.org:uu-186268DiVA: diva2:572813