We study a nonlocal Robin–Venttsel’-type problem for the regional fractional p-Laplacian in an extension domain \(\Omega \) with boundary a d-set. We prove existence and uniqueness of a strong solution via a semigroup approach. Markovianity and ultracontractivity properties are proved. We then consider the elliptic problem. We prove existence, uniqueness and global boundedness of the weak solution.

中文翻译：

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分数$$（{\ varvec {s}}，{\ varvec {p}}）$$（s，p）-Robin–Venttsel在扩展域上的问题

我们研究了具有边界d集的扩展域\（\ Omega \）中的局部分数p -Laplacian的非局部Robin-Venttsel'型问题。我们通过半群方法证明了一个强解决方案的存在性和唯一性。证明了马尔可夫性和超收缩性。然后，我们考虑椭圆问题。我们证明了该弱解的存在性，唯一性和全局有界性。