F. Grube

activity

20242026

collaborators

5 papers

math.AP2026

Boundary regularity for general elliptic operators of order $2 s$

Florian Grube, Xavier Ros-Oton

We establish optimal $C^{s}$ boundary regularity for the most general class of (linear and translation invariant) nonlocal elliptic operator of order $2 s$ . Namely, we consider LÃ©vy…

math.AP2026

A strong-type unique continuation principle for the fractional $p$ -Laplacian

Florian Grube

We provide a simple and direct proof of a strong-type unique continuation principle for the fractional $p$ -Laplacian $(- I^_{p})^{s}$ for a range of $s$ and $p$ . The result extends to s…

math.AP2025

The inhomogeneous fractional Dirichlet problem

Florian Grube

We study boundary regularity for the inhomogeneous Dirichlet problem for $2 s$ -stable operators in generalized HÃ¶lder spaces. Moreover, we provide explicit counterexamples that sho…

math.AP2024

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 $R \times R$ using Fourier methods. Additionally, we provid…

math.AP2024

Boundary regularity and Hopf lemma for nondegenerate stable operators

Florian Grube

We prove sharp boundary H{Ã¶}lder regularity for solutions to equations involving stable integro-differential operators in bounded open sets satisfying the exterior $C^{1,\text{din…

Boundary regularity for general elliptic operators of order 2s

A strong-type unique continuation principle for the fractional p-Laplacian

The inhomogeneous fractional Dirichlet problem

Pointwise estimates of the fundamental solution to the fractional Kolmogorov equation

Boundary regularity and Hopf lemma for nondegenerate stable operators

Boundary regularity for general elliptic operators of order $2 s$

A strong-type unique continuation principle for the fractional $p$ -Laplacian