8 papers · 1 filter
Lipschitz regularity for parabolic double phase equations with gradient nonlinearity
Abhrojyoti Sen, Jarkko Siltakoski
We establish the local Lipschitz regularity in space for the viscosity solutions to the parabolic double phase equation of the form \[ \smash{\partial_{t}u-\operatorname{div} \left…
Existence of variational solutions to doubly nonlinear systems in general noncylindrical domains
Leah Schätzler, Christoph Scheven, Jarkko Siltakoski +1
We consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big( D_ξf(x,u,Du) \big) = -…
Existence of variational solutions to doubly nonlinear systems in nondecreasing domains
Leah Schätzler, Christoph Scheven, Jarkko Siltakoski +1
For , we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form \begin{align*} \partial_t \big( |u|^{q-1}u \big) - \operatorname{div} \big…
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…
The bounded slope condition for parabolic equations with time-dependent integrands
Leah Schätzler, Jarkko Siltakoski
In this paper, we study the Cauchy-Dirichlet problem \begin{equation*} \left\{ \begin{array}{ll} \mbox{ } & \mbox{i…
Equivalence between radial solutions of different non-homogeneous -Laplacian type equations
Jarkko Siltakoski
We study radial viscosity solutions to the equation \[ -\ |Du\ |^{q-2}Δ_{p}^{N}u=f(\ |x\ |)\quad\text{in }B_{R}\subset\mathbb{R}^{N}, \] where , and…