2 citations · 4 across the 9 of their papers we have counts for
10 papers
Boundary regularity for general elliptic operators of order
Florian Grube, Xavier Ros-Oton
We establish optimal boundary regularity for the most general class of (linear and translation invariant) nonlocal elliptic operator of order . Namely, we consider Lévy o…
A strong-type unique continuation principle for the fractional -Laplacian
Florian Grube
We provide a simple and direct proof of a strong-type unique continuation principle for the fractional -Laplacian for a range of and . The result extends to st…
The inhomogeneous fractional Dirichlet problem
Florian Grube
We study boundary regularity for the inhomogeneous Dirichlet problem for -stable operators in generalized Hölder spaces. Moreover, we provide explicit counterexamples that show…
Pointwise estimates of the fundamental solution to the fractional Kolmogorov equation
Florian Grube
We prove sharp two-sided estimates of the fundamental solution to the fractional Kolmogorov equation in using Fourier methods. Additionally, we provid…
Boundary regularity and Hopf lemma for nondegenerate stable operators
Florian Grube
We prove sharp boundary H{ö}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{dini…
The Dirichlet Problem for Lévy-stable operators with -data
Florian Grube, Thorben Hensiek, Waldemar Schefer
We prove Sobolev regularity for distributional solutions to the Dirichlet problem for generators of -stable processes and exterior data, inhomogeneity in weighted -spaces.…
Robust nonlocal trace and extension theorems
Florian Grube, Moritz Kassmann
We prove trace and extension results for Sobolev-type function spaces that are well suited for nonlocal Dirichlet and Neumann problems including those for the fractional -Laplac…
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…
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…
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)…