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math.AP2022★ 2 cited
Robust nonlocal trace spaces and Neumann problems
Florian Grube, Thorben Hensiek
We prove trace and extension results for fractional Sobolev spaces of order . These spaces are used in the study of nonlocal Dirichlet and Neumann problems on bounded do…
math.AP2022
Maximum principle for stable operators
Florian Grube, Thorben Hensiek
We prove a weak maximum principle for nonlocal symmetric stable operators. This includes the fractional Laplacian. The main focus of this work is the regularity of the considered f…
math.AP2022
Norm inflation for the Zakharov system
Florian Grube
The Cauchy problem for the classical Zakharov system is shown to be ill-posed in the sense of norm inflation in a range of Sobolev spaces $H^s(\mathbb{R}^d)\times H^l(\mathbb{R}^d)…