7 citations · 15 across the 20 of their papers we have counts for
5 papers · 2 filters
Approximation of BV functions by neural networks: A regularity theory approach
Benny Avelin, Vesa Julin
In this paper we are concerned with the approximation of functions by single hidden layer neural networks with ReLU activation functions on the unit circle. In particular, we are i…
Stationary sets of the mean curvature flow with a forcing term
Vesa Julin, Joonas Niinikoski
We consider the flat flow approach for the mean curvature equation with forcing in an Euclidean space of dimension at least 2. Our main results states that tangential…
Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow
Vesa Julin, Joonas Niinikoski
We prove a new quantitative version of the Alexandrov theorem which states that if the mean curvature of a regular set in R^{n+1} is close to a constant in L^{n}-sense, then the se…
Stationary sets and asymptotic behavior of the mean curvature flow with forcing in the plane
Nicola Fusco, Vesa Julin, Massimiliano Morini
We consider the flat flow solutions of the mean curvature equation with a forcing term in the plane. We prove that for every constant forcing term the stationary sets are given by…
Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
Vesa Julin, Giorgio Saracco
We provide a quantitative lower bound to the Cheeger constant of a set in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide exampl…