Harnack inequality for harmonic functions relative to a nonlinear p-homogeneous Riemannian Dirichlet form
Abstract
We consider a measure valued map α(u) defined on D where D is a subspace of L^p(X,m) with X a locally compact Hausdorff topological space with a distance under which it is a space of homogeneous type. Under assumptions of convexity, Gateaux differentiability and other assumptions on α which generalize the properties of the energy measure of a Dirichlet form, we prove the Holder continuity of the local solution u of the problem∫Xµ(u,v)(dx) = 0 for each v belonging to a suitable space of test functions, where µ(u,v) =< α'(u),v >.
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