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math.AP2024
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…
math.AP2024
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…