Given a bounded Lipschitz domain , , we prove~that the Poisson's problem for the Laplacian with right-hand side in , Robin-type boundary datum in the Besov space and non-negative, non-everywhere vanishing Robin coefficient , is uniquely solvable in the class for , where () is an open (,)-dependent plane region and is to be interpreted ad the common (optimal) solvability region for all Lipschitz domains. We prove a similar regularity result for the Poisson's problem for the 3-dimensional Lamé System with traction-type Robin boundary condition. All solutions are expressed as boundary layer potentials.
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Loredana Lanzani, Osvaldo Méndez, The Poisson’s problem for the Laplacian with Robin boundary condition in non-smooth domains. Rev. Mat. Iberoam. 22 (2006), no. 1, pp. 181–204