The L^p Dirichlet Problem and Nondivergence Harmonic Measure

Details The L^p Dirichlet Problem and Nondivergence Harmonic Measure The L^p Dirichlet Problem and Nondivergence Harmonic Measure

2002-04-04

arxiv.org/abs/math/0204055v2

Mathematics

Analysis of PDEs

23 pages, LaTeX, Transactions AMS format

Scientific paper

We consider the Dirichlet problem Lu = 0 in D u = g on E = boundary of D for two second order elliptic operators L_k(u) = \sum_{i,j=1}^n a_k^{ij}(x) \partial_{ij} u(x), k=0,1, in a bounded Lipschitz domain D in R^n. The coefficients a_k^{ij} belong to the space of bounded mean oscillation BMO with a suitable small BMO modulus. We assume that L_0 is regular in L^p(E,ds) for some p, 1

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