10 citations · 20 across the 13 of their papers we have counts for
14 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…
Solutions to the nonlinear obstacle problem with compact contact sets
Simon Eberle, Hui Yu
For the obstacle problem with a nonlinear operator, we characterize the space of global solutions with compact contact sets. This is achieved by constructing a bijection onto a cla…
Compact contact sets of sub-quadratic solutions to the thin obstacle problem
Simon Eberle, Hui Yu
We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution…
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…