11 citations · 41 across the 27 of their papers we have counts for
6 papers · 2 filters
Boundary regularity for parabolic systems in convex domains
Verena Bögelein, Frank Duzaar, Naian Liao +1
In a cylindrical space-time domain with a convex, spatial base, we establish a local Lipschitz estimate for weak solutions to parabolic systems with Uhlenbeck structure up to the l…
Continuity of the temperature in a multi-phase transition problem
Ugo Gianazza, Naian Liao
Locally bounded, local weak solutions to a doubly nonlinear parabolic equation, which models the multi-phase transition of a material, is shown to be locally continuous. Moreover,…
On the Hölder regularity of signed solutions to a doubly nonlinear equation. Part III
Naian Liao, Leah Schätzler
We establish the local Hölder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is \[ \partial_t\big(|u|^{q-1}u\big)…
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…
Local continuity of weak solutions to the Stefan problem involving the singular -Laplacian
Naian Liao
We establish the local continuity of locally bounded weak solutions (temperatures) to the doubly singular parabolic equation modeling the phase transition of a material: \[ \partia…
On the logarithmic type boundary modulus of continuity for the Stefan problem
Naian Liao
A logarithmic type modulus of continuity is established for weak solutions to a two-phase Stefan problem, up to the parabolic boundary of a cylindrical space-time domain. For the D…