Regularity results for nonlocal evolution Venttsel’ problems
2020 ◽
Vol 23
(5)
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pp. 1416-1430
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Keyword(s):
A Priori
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Abstract We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and regularity in (anisotropic) weighted Sobolev spaces of the solution. The nonlocal term can be regarded as a regional fractional Laplacian on the boundary. The regularity results deeply rely on a priori estimates, obtained via the so-called Munchhausen trick, and sophisticated extension theorem for anisotropic weighted Sobolev spaces.