5 papers
Trudinger's Parabolic Equation
Peter Lindqvist, Mikko Parviainen, Saara Sarsa
We study the uniqueness of non-negative solutions of the equation \begin{align*} \partial_t\left(|u|^{p-2}u\right)\,=\, \operatorname{div}(|\nabla u|^{p-2}\nabla u). \end{align*} B…
Uniqueness of sign-changing solutions to Trudinger's equation
Riku Anttila, Peter Lindqvist, Mikko Parviainen
We establish uniqueness for sign-changing solutions to Trudinger's parabolic equation with time dependent Dirichlet boundary data.
Lipschitz continuity and equivalence of positive viscosity and weak solutions to Trudinger's equation
Peter Lindqvist, Mikko Parviainen, Jarkko Siltakoski
We show that stricty positive viscosity supersolutions to Trudinger's equation are local weak supersolutions when . As an application, we show using the Ishii-Lions met…
Connections between coupling and Ishii-Lions methods for tug-of-war with noise stochastic games
Riku Anttila, Juan J. Manfredi, Mikko Parviainen
We present a streamlined account of two different regularity methods as well as their connections. We consider the coupling method in the context of tug-of-war with noise stochasti…
Krylov-Safonov theory for Pucci-type extremal inequalities on random data clouds
Ãngel Arroyo, Pablo Blanc, Mikko Parviainen
We establish Krylov-Safonov type Hölder regularity theory for solutions to quite general discrete dynamic programming equations or equivalently discrete stochastic processes on ra…