6 papers
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 righ…
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 , , a…
Regularity theory for sub-critical -parabolic systems with measurable coefficients
Verena Bögelein, Frank Duzaar, Ugo Gianazza +1
A quantitative regularity theory is developed for weak solutions to the parabolic system $$ \partial_t u-\mathrm{div}\,{\boldsymbol{\mathsf A}}(x,t,Du)=0 \quad\text{in }E_T\subset…
Parabolic PDEs with Dynamic Data under a Bounded Slope Condition
Verena Bögelein, Frank Duzaar, Giulia Treu
We establish the existence of Lipschitz continuous solutions to the Cauchy Dirichlet problem for a class of evolutionary partial differential equations of the form $$ \partial_tu-\…
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 w…
Local boundedness and higher integrability for the sub-critical singular porous medium system
Verena Bögelein, Frank Duzaar, Ugo Gianazza +1
The gradient of weak solutions to porous medium-type equations or systems possesses a higher integrability than the one assumed in the pure notion of a solution. We settle the crit…