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.

Regularity results for nonlocal evolution Venttsel' problems / Creo, S.; Lancia, M. R.; Nazarov, A. I.. - In: FRACTIONAL CALCULUS & APPLIED ANALYSIS. - ISSN 1311-0454. - 23:5(2020), pp. 1416-1430. [10.1515/fca-2020-0070]

Regularity results for nonlocal evolution Venttsel' problems

Creo S.
;
Lancia M. R.;
2020

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.
anisotropic weighted Sobolev spaces; nonlocal operators; piecewise smooth domains; Venttsel' problems
01 Pubblicazione su rivista::01a Articolo in rivista
Regularity results for nonlocal evolution Venttsel' problems / Creo, S.; Lancia, M. R.; Nazarov, A. I.. - In: FRACTIONAL CALCULUS & APPLIED ANALYSIS. - ISSN 1311-0454. - 23:5(2020), pp. 1416-1430. [10.1515/fca-2020-0070]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1463762
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