The Lp Poisson-Robin and Poisson-Robin-regularity problems are equivalent (via duality and with the classical Robin plus Dirichlet problems), and for the Laplacian on Lipschitz domains they are solvable in sharp ranges of p.
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Equivalent Characterizations and Their Applications of Solvability of $L^p$ Poisson--Robin(-Regularity) Problems on Rough Domains
The Lp Poisson-Robin and Poisson-Robin-regularity problems are equivalent (via duality and with the classical Robin plus Dirichlet problems), and for the Laplacian on Lipschitz domains they are solvable in sharp ranges of p.