Naian Liao

collaborators

7 papers

math.AP2026

Sharp gradient integrability for $(s, p)$ -Poisson type equations

Verena BÃ¶gelein, Frank Duzaar, Naian Liao +1

We prove local $W^{1, q}$ -regularity for weak solutions to fractional $p$ -Laplacian type equations with right-hand side $f \in L_{loc}^{r} (I^c ◯)$ . Assuming $p > 1$ , $s \in (0, 1)$ , a…

math.AP2026

Regularity theory for sub-critical $p$ -parabolic systems with measurable coefficients

Verena BÃ¶gelein, 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…

math.AP2025

Nonnegative solutions to nonlocal parabolic equations

Naian Liao, Marvin Weidner

We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a…

math.AP2025

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…

math.AP2025

Gradient estimates for the fractional $p$ -Poisson equation

Verena BÃ¶gelein, Frank Duzaar, Naian Liao +1

We consider local weak solutions to the fractional $p$ -Poisson equation of order $s$ , i.e. $(- I^_{p})^{s} u = f$ . In the range $p > 1$ and $s \in (\frac{p - 1}{p}, 1)$ w…

math.AP2025

Local boundedness and higher integrability for the sub-critical singular porous medium system

Verena BÃ¶gelein, 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…

Sharp gradient integrability for (s,p)-Poisson type equations

Regularity theory for sub-critical p-parabolic systems with measurable coefficients

Nonnegative solutions to nonlocal parabolic equations

Time-insensitive nonlocal parabolic Harnack estimates

Gradient estimates for the fractional p-Poisson equation

Local boundedness and higher integrability for the sub-critical singular porous medium system

Sharp gradient integrability for $(s, p)$ -Poisson type equations

Regularity theory for sub-critical $p$ -parabolic systems with measurable coefficients

Gradient estimates for the fractional $p$ -Poisson equation