Approximation of BV functions by neural networks: A regularity theory approach

no code implementations • 15 Dec 2020 • Benny Avelin, Vesa Julin

We first study the convergence to equilibrium of the stochastic gradient flow associated with the cost function with a quadratic penalization.

Stationary sets of the mean curvature flow with a forcing term

no code implementations • 27 Nov 2020 • Vesa Julin, Joonas Niinikoski

We consider the flat flow approach for the mean curvature equation with forcing in an Euclidean space $\mathbb R^n$ of dimension at least 2.

Analysis of PDEs 35J93