6 papers
Higher integrability for parabolic double phase equations with an improved gap bound
Abhrojyoti Sen, Jarkko Siltakoski
We prove a local higher integrability result for the gradient of Hölder continuous weak solutions to the parabolic double phase equation \[ \partial_t u - \operatorname{div} \left…
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 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…
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…
Intrinsic Harnack's inequality for a general nonlinear parabolic equation in non-divergence form
Tapio Kurkinen, Jarkko Siltakoski
We prove the intrinsic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic -Laplace equation and the normalized version…
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) = -…