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math.AP2026
Existence and uniqueness of weak solutions to quasilinear PDEs with critical data
Pascal Auscher, Sebastian Bechtel
We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreov…
math.AP2026
An extended variational setting for critical SPDEs with Lévy noise
Sebastian Bechtel, Fabian Germ, Mark Veraar
The critical variational setting was recently introduced and shown to be applicable to many important SPDEs not covered by the classical variational setting. In this paper, we exte…
math.AP2026★ 5 cited
Counterexamples to maximal regularity for operators in divergence form
Sebastian Bechtel, Connor Mooney, Mark Veraar
In this paper, we present counterexamples to maximal -regularity for a parabolic PDE. The example is a second-order operator in divergence form with space and time-dependent c…