1 citations · 2 across the 14 of their papers we have counts for
16 papers
Calderón-Zygmund estimates for parabolic systems with -growth and non-divergence data
Pêdra Andrade, Kristian Moring
We obtain Calderón--Zygmund estimates for weak solutions to nonlinear parabolic systems with polynomial -growth and the right-hand side in non-divergence form. Our approach does…
Calderón-Zygmund estimates for parabolic -Laplacian systems with non-divergence form right-hand sides
Pêdra Andrade, Verena Bögelein, Frank Duzaar +1
We establish local Calderón-Zygmund type estimates for weak solutions to nonlinear parabolic systems with -growth and VMO coefficients. In particular, we prove that if the right…
Sharp gradient integrability for -Poisson type equations
Verena Bögelein, Frank Duzaar, Naian Liao +1
We prove local -regularity for weak solutions to fractional -Laplacian type equations with right-hand side . Assuming , , an…
Global higher integrability for systems with -growth structure in noncylindrical domains
Kristian Moring, Christoph Scheven, Leah Schätzler
We consider the Cauchy-Dirichlet problem to systems with -growth structure with , whose prototype is \begin{equation*} \partial_t u- \operatorname{div} \big( |Du…
Gradient estimates for the fractional -Poisson equation
Verena Bögelein, Frank Duzaar, Naian Liao +1
We consider local weak solutions to the fractional -Poisson equation of order , i.e. . In the range and we…
On notions of -parabolic capacity and applications
Kristian Moring, Christoph Scheven
We consider different notions of capacity related to the parabolic -Laplace equation. Our focus is on a variational notion, which is consistent in the full range . F…
Hölder regularity for degenerate parabolic double-phase equations
Wontae Kim, Kristian Moring, Lauri Särkiö
We prove that bounded weak solutions to degenerate parabolic double-phase equations of -Laplace type are locally Hölder continuous. The proof is based on phase analysis and meth…
Higher integrability for singular doubly nonlinear systems
Kristian Moring, Leah Schätzler, Christoph Scheven
We prove a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems whose prototype is $$ \partial_t \left(|u|^{q-1}u \rig…
Supercaloric functions for the porous medium equation in the fast diffusion case
Kristian Moring, Christoph Scheven
We study a generalized class of supersolutions, so-called supercaloric functions to the porous medium equation in the fast diffusion case. Supercaloric functions are defined as low…
On two notions of solutions to the obstacle problem for the singular porous medium equation
Kristian Moring, Christoph Scheven
We show that two different notions of solutions to the obstacle problem for the porous medium equation, a potential theoretic notion and a notion based on a variational inequality,…
Continuity up to the boundary for obstacle problems to porous medium type equations
Kristian Moring, Leah Schätzler
We show that signed weak solutions to obstacle problems for porous medium type equations with Cauchy-Dirichlet boundary data are continuous up to the parabolic boundary, provided t…
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…
On the Hölder regularity for obstacle problems to porous medium type equations
Kristian Moring, Leah Schätzler
We show that signed weak solutions to parabolic obstacle problems with porous medium type structure are locally Hölder continuous, provided that the obstacle is Hölder continuous.
Supercaloric functions for the parabolic -Laplace equation in the fast diffusion case
Ratan Kr. Giri, Juha Kinnunen, Kristian Moring
We study a generalized class of supersolutions, so-called -supercaloric functions, to the parabolic -Laplace equation. This class of functions is defined as lower semicontinu…
Stability for systems of porous medium type
Kristian Moring, Rudolf Rainer
We establish stability properties of weak solutions for systems of porous medium type with respect to the exponent . Thereby we treat stability for the local case as well as for…
Global higher integrability of weak solutions of porous medium systems
Kristian Moring, Christoph Scheven, Sebastian Schwarzacher +1
We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by \begin{equation*} \partial_t u-Δ(|u|^…