46 citations · 162 across the 32 of their papers we have counts for
24 papers · 1 filter
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…
Gradient higher integrability for double phase problems on metric measure spaces
Juha Kinnunen, Antonella Nastasi, Cintia Pacchiano Camacho
We study local and global higher integrability properties for quasiminimizers of a class of double-phase integrals characterized by nonstandard growth conditions. We work purely on…
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…
Parabolic Muckenhoupt Weights on Spaces of Homogeneous Type
Juha Kinnunen, Kim Myyryläinen, Dachun Yang +1
This work discusses parabolic Muckenhoupt weights on spaces of homogeneous type, i.e.\ quasi-metric spaces with both a doubling measure and an additional monotone geodesic property…
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…