4 papers
Graph-Theoretic Detection of Hilbert Space Fragmentation
A. Rutkowski, M. Mierzejewski, J. Herbrych
Hilbert-space fragmentation provides a mechanism for ergodicity breaking in quantum many-body systems even in the absence of disorder, leading to dynamically disconnected sectors a…
A Schauder regularity theory for nonlocal and mixed local-nonlocal viscous Hamilton$\unicode{x2013}$Jacobi equations
Espen Robstad Jakobsen, Robin Østern Lien, Artur Rutkowski
We prove space-time Schauder estimates $\unicode{x2013}$ optimal regularity estimates in Hölder spaces $\unicode{x2013}$ and well-posedness results for mild and classical solutions…
Equivalence of definitions of fractional caloric functions
Artur Rutkowski
We prove equivalence between nonnegative distributional solutions of the fractional heat equation and caloric functions, i.e., functions satisfying the mean value property with res…
Towards a Schauder theory for fractional viscous Hamilton--Jacobi equations
Espen R. Jakobsen, Artur Rutkowski
We survey some results on Lipschitz and Schauder regularity estimates for viscous Hamilton--Jacobi equations with subcritical Lévy diffusions. The Schauder estimates, along with ex…