46 citations · 162 across the 32 of their papers we have counts for
8 papers · 1 filter
Variational solutions to the total variation flow on metric measure spaces
Vito Buffa, Juha Kinnunen, Cintia Pacchiano Camacho
We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincaré inequality. We apply the concept of parabolic D…
On the regularity theory for mixed local and nonlocal quasilinear parabolic equations
Prashanta Garain, Juha Kinnunen
We consider mixed local and nonlocal quasilinear parabolic equations of -Laplace type and discuss several regularity properties of weak solutions for such equations. More precis…
Characterizations of weak reverse Hölder inequalities on metric measure spaces
Juha Kinnunen, Emma-Karoliina Kurki, Carlos Mudarra
We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among other…
Dyadic John-Nirenberg space
Juha Kinnunen, Kim Myyryläinen
We discuss the dyadic John-Nirenberg space that is a generalization of functions of bounded mean oscillation. A John-Nirenberg inequality, which gives a weak type estimate for the…
On the definition of solution to the total variation flow
Juha Kinnunen, Christoph Scheven
We show that the notions of weak solution to the total variation flow based on the Anzellotti pairing and the variational inequality coincide under some restrictions on the boundar…
Weak Harnack inequality for a mixed local and nonlocal parabolic equation
Prashanta Garain, Juha Kinnunen
This article proves a weak Harnack inequality with a tail term for sign changing supersolutions of a mixed local and nonlocal parabolic equation. Our argument is purely analytic. I…