30 citations · 87 across the 26 of their papers we have counts for
26 papers
ACF Almost Monotonicity at Infinity with Applications to Perturbed Global Solutions
Simon Eberle, Anthony Salib, Georg S. Weiss +1
We study the large-scale behavior of the coincidence set of perturbations of global solutions to the classical obstacle problem in , with blow-down invar…
Complete classification of global solutions to the obstacle problem
Simon Eberle, Alessio Figalli, Georg S. Weiss
The characterization of global solutions to the obstacle problems in , or equivalently of null quadrature domains, has been studied over more than 90 years. In this p…
Normalized gradient flow optimization in the training of ReLU artificial neural networks
Simon Eberle, Arnulf Jentzen, Adrian Riekert +1
The training of artificial neural networks (ANNs) is nowadays a highly relevant algorithmic procedure with many applications in science and industry. Roughly speaking, ANNs can be…
The structure of the regular part of the free boundary close to singularities in the obstacle problem
Simon Eberle, Henrik Shahgholian, Georg Sebastian Weiss
We prove the -- to the best knowledge of the authors -- first result on the fine asymptotic behavior of the regular part of the free boundary of the obstacle problem close to singu…
Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation
Simon Eberle, Arnulf Jentzen, Adrian Riekert +1
The training of artificial neural networks (ANNs) with rectified linear unit (ReLU) activation via gradient descent (GD) type optimization schemes is nowadays a common industrially…
Regularity of the free boundary for a parabolic cooperative system
Gohar Aleksanyan, Morteza Fotouhi, Henrik Shahgholian +1
In this paper we study the following parabolic system \begin{equation*} Δ\u -\partial_t \u =|\u|^{q-1}\u\,χ_{\{ |\u|>0 \}}, \qquad \u = (u^1, \cdots , u^m) \ , \end{equation*} with…