7 citations · 12 across the 6 of their papers we have counts for
9 papers · 1 filter
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…
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…
Short time existence of the classical solution to the fractional Mean curvature flow
Vesa Julin, Domenico La Manna
We establish short-time existence of the smooth solution to the fractional mean curvature flow when the initial set is bounded and C^{1,1}-regular. We provide the same result also…
The surface diffusion flow with elasticity in three dimensions
Nicola Fusco, Vesa Julin, Massimiliano Morini
We establish short-time existence of a smooth solution to the surface diffusion equation with an elastic term and without an additional curvature regularization in three space dime…
Nonlinear stability results for the modified Mullins-Sekerka and the surface diffusion flow
Emilio Acerbi, Nicola Fusco, Vesa Julin +1
It is shown that any three-dimensional periodic configuration that is strictly stable for the area functional is exponentially stable for the surface diffusion flow and for the Mul…