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Regularity results for nonlocal evolution Venttsel’ problems
Fractional Calculus and Applied Analysis ( IF 3 ) Pub Date : 2020-10-01 , DOI: 10.1515/fca-2020-0070
Simone Creo 1 , Maria Rosaria Lancia 1 , Alexander I. Nazarov 2, 3
Affiliation  

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.

中文翻译:

非局部演化 Venttsel 问题的规律性结果

摘要 我们考虑多边形和分段光滑二维域中的抛物线非局部文特塞尔问题,并研究解的(各向异性)加权 Sobolev 空间中的存在性、唯一性和规律性。非局部项可以看作是边界上的区域分数拉普拉斯算子。规律性结果很大程度上依赖于通过所谓的 Munchhausen 技巧获得的先验估计,以及各向异性加权 Sobolev 空间的复杂扩展定理。
更新日期:2020-10-01
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