Research Interests


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

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