### Research Interests

- Partial Differential Equations
- Nonlocal Traces
- Mosco Convergence
- Regularity Theory
- Norm Inflation For Evolution Equations
- Zakharov System

### Preprints

#### Robust nonlocal trace spaces and Neumann problems

We prove trace and extension results for fractional Sobolev spaces of order $s\in(0,1)$. These spaces are used in the study of nonlocal Dirichlet and Neumann problems on bounded domains. The results are robust in the sense that the continuity of the trace and extension operators is uniform as s approaches 1 and our trace spaces converge to $H^{1/2}(\partial \Omega)$. We apply these results in order to study the convergence of solutions of nonlocal Neumann problems as the integro-differential operators localize to a symmetric, second order operator in divergence form. *T. Hensiek, FG* (2022)
arXiv

#### Maximum principle for stable operators

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 function. *T. Hensiek, FG* (2022)
arXiv

#### Norm inflation for the Zakharov system

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 for all dimensions d. This proves several results on well-posedness, which includes existence of solutions, uniqueness and continuous dependence on the initial data, to be sharp up to endpoints. *FG* (2022)
arXiv