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SOLUTIONS TO THE NONLINEAR OBSTACLE PROBLEM WITH COMPACT CONTACT SETS

Eberle, S.; Yu, H. (2023-01-01)

For the obstacle problem with a nonlinear operator, we character- ize the space of global solutions with compact contact sets. This is achieved by constructing a bijection onto a class of quadratic polynomials describing ...

Normalized gradient flow optimization in the training of ReLU artificial neural networks

Eberle, S.; Jentzen, A.; Riekert, A.; Weiss, G. (2022-01-01)

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 regarded as iterated compositions between ...

COMPLETE CLASSIFICATION OF GLOBAL SOLUTIONS TO THE OBSTACLE PROBLEM

Eberle, S.; Figalli, A.; Weiss, G.S. (2022-01-01)

The characterization of global solutions to the obstacle problems in RN , or equivalently of null quadrature domains, has been studied over more than 90 years. In this paper we give a conclusive answer to this problem by p...

COMPACT CONTACT SETS OF SUB-QUADRATIC SOLUTIONS TO THE THIN OBSTACLE PROBLEM

Eberle, S.; Yu, H. (2023-01-01)

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. On the other hand, if such a solution h...