Benjamin Scharf

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In this paper, we study the regularity of solutions to the p-Poisson equation for all 1 < p < ∞. In particular, we are interested in smoothness estimates in the adaptivity scale B σ τ (L τ (Ω)), 1/τ = σ/d + 1/p, of Besov spaces. The regularity in this scale determines the order of approximation that can be achieved by adaptive and other nonlinear(More)
For high dimensional particle systems, governed by smooth nonlinearities depending on mutual distances between particles, one can construct low-dimensional representations of the dynamical system, which allow the learning of nearly optimal control strategies in high dimension with overwhelming confidence. In this paper we present an instance of this general(More)
Collective migration of animals in a cohesive group is rendered possible by a strategic distribution of tasks among members: some track the travel route, which is time and energy-consuming, while the others follow the group by interacting among themselves. In this paper, we study a social dynamics system modeling collective migration. We consider a group of(More)
A rather tricky question is the construction of wavelet bases on domains for suitable function spaces (Sobolev, Besov, Triebel-Lizorkin type). In his monograph from 2008, Triebel presented an approach how to construct wavelet (Riesz) bases in function spaces of Besov and Triebel-Lizorkin type on cellular domains , in particular on the cube. However, he had(More)
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