Naian Liao

activity

20132026

most citedA Boundary Estimate for Singular Parabolic Diffusion Equations

11 citations · 41 across the 27 of their papers we have counts for

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Showing 2026 · math.APShow all

3 papers · 2 filters

math.AP2026

Nonlocal intrinsic Harnack estimates

Naian Liao

We extend DiBenedetto's intrinsic parabolic Harnack estimates to a class of integro-differential equations with measurable kernels modeled on the fractional $p$ -Laplacian. More rem…

math.AP2026

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

Verena Bögelein, 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 $f \in L_{loc}^{r} (Ω)$ . Assuming $p > 1$ , $s \in (0, 1)$ , an…

math.AP2026

Regularity theory for sub-critical $p$ -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…

Nonlocal intrinsic Harnack estimates

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

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

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

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