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math.AP2026
Sharp local sparsity of regularized optimal transport
Alberto González-Sanz, Rishabh S. Gvalani, Lukas Koch
In recent years, the use of entropy-regularized optimal transport with -type entropies has become increasingly popular. In this setting, the solutions are sparse, in the sense…
math.AP2024
On the Lavrentiev gap for convex, vectorial integral functionals
Lukas Koch, Matthias Ruf, Mathias Schäffner
We prove the absence of a Lavrentiev gap for vectorial integral functionals of the form $$ F: g+W_0^{1,1}(Ω)^m\to\mathbb{R}\cup\{+\infty\},\qquad F(u)=\int_ΩW(x,\mathrm{D} u)\,\m…
math.AP2024
A note on improved differentiability for the Banach-space valued Finsler -Laplacian
Max Goering, Lukas Koch
We obtain improved fractional differentiability of solutions to the Banach-space valued Finsler -Laplacian defined on a -convex, -smooth Banach space. The operators we…