46 citations · 162 across the 32 of their papers we have counts for
6 papers · 2 filters
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…
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…
On the regularity theory for mixed local and nonlocal quasilinear elliptic equations
Prashanta Garain, Juha Kinnunen
We consider a combination of local and nonlocal -Laplace equations and discuss several regularity properties of weak solutions. More precisely, we establish local boundedness of…
Lower semicontinuity and pointwise behavior of supersolutions for some doubly nonlinear nonlocal parabolic -Laplace equations
Agnid Banerjee, Prashanta Garain, Juha Kinnunen
We discuss pointwise behavior of weak supersolutions for a class of doubly nonlinear parabolic fractional -Laplace equations which includes the fractional parabolic -Laplace…