11 citations · 41 across the 27 of their papers we have counts for
6 papers · 2 filters
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,…
Time-insensitive nonlocal parabolic Harnack estimates
Naian Liao, Marvin Weidner
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal…
Improved moduli of continuity for degenerate phase transitions
Ugo Gianazza, Naian Liao, José Miguel Urbano
We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the -dimensional, two-phase Stefan problem featuring a deg…
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…
Harnack estimates for nonlocal drift-diffusion equations
Naian Liao
A set of pointwise estimates are established for local solutions to nonlocal diffusion equations with a drift term. In particular, our Harnack estimates are the first ones for such…
On the modulus of continuity of solutions to nonlocal parabolic equations
Naian Liao
A general modulus of continuity is quantified for locally bounded, local, weak solutions to nonlocal parabolic equations, under a minimal tail condition. Hölder modulus of continui…