9 papers
Parabolic Poincaré inequalities and maximal function estimates for systems of partial differential equations
Wontae Kim, Juha Kinnunen
We study parabolic Poincaré inequalities for solutions to nonlinear systems of partial differential equations. Our main results show that these inequalities are self-improving. As…
Borderline gradient regularity estimates for quasilinear parabolic systems with data independent of time
Karthik Adimurthi, Wontae Kim
In this paper, we study some regularity issues concerning the gradient of weak solutions of , where is mo…
Calderón-Zygmund type estimate for the parabolic double-phase system
Wontae Kim
This paper provides a local and global Calderón-Zygmund type estimate of a weak solution to the parabolic double-phase system. The proof of local estimate is based on comparison es…
Lipschitz truncation method for parabolic double-phase systems and applications
Wontae Kim, Juha Kinnunen, Lauri Särkiö
We discuss a Lipschitz truncation technique for parabolic double-phase problems of -Laplace type in order to prove energy estimates and uniqueness results for the Dirichlet prob…
On the regularity theory for mixed anisotropic and nonlocal -Laplace equations and its applications to singular problems
Prashanta Garain, Wontae Kim, Juha Kinnunen
We establish existence results for a class of mixed anisotropic and nonlocal -Laplace equation with singular nonlinearities. We consider both constant and variable singular expo…
Self-improving properties of very weak solutions to double phase systems
Sumiya Baasandorj, Sun-Sig Byun, Wontae Kim
We prove the self-improving property of very weak solutions to non-uniformly elliptic problems of double phase type in divergence form under sharp assumptions on the nonlinearity.
Gradient higher integrability for degenerate parabolic double-phase systems
Wontae Kim, Juha Kinnunen, Kristian Moring
We prove local higher integrability of the gradient of a weak solution to a degenerate parabolic double-phase system. This result comes with a reverse Hölder type estimate for the…
An existence result for nonhomogeneous quasilinear parabolic equations beyond the duality pairing
Karthik Adimurthi, Sun-Sig Byun, Wontae Kim
In this paper, we prove existence of \emph{very weak solutions} to nonhomogeneous quasilinear parabolic equations beyond the duality pairing. The main ingredients are a priori esit…
Partial existence result for Homogeneous Quasilinear parabolic problems beyond the duality pairing
Karthik Adimurthi, Sun-Sig Byun, Wontae Kim
In this paper, we study the existence of distributional solutions solving \cref{main-3} on a bounded domain satisfying a uniform capacity density condition where the nonlinear…