Regularity Results for Nonlocal Evolution Venttsel’ Problems

Regularity Results for Nonlocal Evolution Venttsel’ Problems

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. T...

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Veröffentlicht in:Fractional calculus & applied analysis 2020-10, Vol.23 (5), p.1416-1430
Hauptverfasser: Creo, Simone, Lancia, Maria Rosaria, Nazarov, Alexander I.
Format: Artikel
Sprache:eng
Schlagworte:
35B45
35B65
Abstract Harmonic Analysis
Analysis
anisotropic weighted Sobolev spaces
Functional Analysis
Integral Transforms
Mathematics
nonlocal operators
Operational Calculus
piecewise smooth domains
Primary 35K20
Regularity
Research Paper
Secondary 335R02
Sobolev space
Venttsel’ problems
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Beschreibung
Zusammenfassung: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. MSC 2010 : Primary 35K20, 35B65; Secondary 335R02, 35B45
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2020-0070