For degenerate elliptic operators on domains with mixed-dimensional boundaries, L^p solvability of the Dirichlet problem is shown equivalent to Poisson-Dirichlet and Poisson-regularity solvability.
Estimates of harmonic measure
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Solvability of the Poisson-Dirichlet problem in domains with boundaries of mixed dimension
For degenerate elliptic operators on domains with mixed-dimensional boundaries, L^p solvability of the Dirichlet problem is shown equivalent to Poisson-Dirichlet and Poisson-regularity solvability.