13 citations · 22 across the 8 of their papers we have counts for
8 papers
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…
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…
Gradient regularity for -harmonic functions
Verena Bögelein, Frank Duzaar, Naian Liao +2
We study the local regularity properties of -harmonic functions, i.e. local weak solutions to the fractional -Laplace equation of order in the case $p\in (1,…
Regularity for the fractional -Laplace equation
Verena Bögelein, Frank Duzaar, Naian Liao +2
Higher Sobolev and Hölder regularity is studied for local weak solutions of the fractional -Laplace equation of order in the case . Depending on the regime considere…
Hölder Continuity of the Gradient of Solutions to Doubly Non-Linear Parabolic Equations
Verena Bögelein, Frank Duzaar, Ugo Gianazza +2
This paper is devoted to studying the local behavior of non-negative weak solutions to the doubly non-linear parabolic equation \begin{equation*} \partial_t u^q - \text{div}\big(|D…
On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part II
Verena Bögelein, Frank Duzaar, Naian Liao +1
We demonstrate two proofs for the local Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\bi…
On the Hölder regularity of signed solutions to a doubly nonlinear equation
Verena Bögelein, Frank Duzaar, Naian Liao
We establish the interior and boundary Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big…
Global gradient bounds for the parabolic p-Laplacian system
Verena Bögelein
A by now classical result due to DiBenedetto states that the spatial gradient of solutions to the parabolic -Laplacian system is locally Hölder continuous in the interior. Howev…