Fa Peng

activity

20192026

most citedOptimal regularity & Liouville property for stable solutions to semilinear elliptic equations in

R^{n}

with

n \geq 10

4 citations · 8 across the 11 of their papers we have counts for

collaborators

12 papers

math.AP2026

The $L^{p}$ Neumann problem for the Stokes system in nonsmooth domains

Qianyun Miao, Fa Peng

We study the $L^{p}$ Neumann problem for the Stokes system on bounded Lipschitz domains in $R^{n}$ with $n \geq 2$ . Our main contribution is to introduce a nonlinear gradient qua…

math.AP2026

Maximal Sobolev regularity of the stress tensor for the symmetric gradient p-Laplace system

Linus Behn, Andrea Cianchi, Lars Diening +1

The symmetric $p$ -Laplace operator enters various models in mathematical physics, such as incompressible materials with power-type hardening and non-Newtonian fluids. In this work,…

math.AP2026

Regularity of stable radial solutions to semilinear elliptic equations in MEMS problems

Fa Peng, Salvador Villegas

This paper investigates the regularity of stable radial solutions to semilinear elliptic equations arising in MEMS problems, modeled by the Dirichlet problem $- Δ u = f (u)$ in the unit…

math.AP2024

A nonlinear Calderón-Zygmund $L^{2}$ -theory for the Dirichlet problem involving $- ∣ D u ∣^{γ} Δ_{p}^{N} u = f$

Qianyun Miao, Fa Peng, Yuan Zhou

We establish a nonlinear Calderón-Zygmund $L^{2}$ -theory to the Dirichlet problem $$-|Du|^γΔ^N_p u=f\in L^2(Ω)\quad {\rm in}\quad Ω; \quad u=0 \ \mbox{on $\partialΩ$} $$ for $n \geq 2$ ,…

math.AP2023

Regularity from $p$ -harmonic potentials to $\infty$ -harmonic potentials in convex rings

Fa Peng, Yi Ru-Ya Zhang, Yuan Zhou

The exploration of shape metamorphism, surface reconstruction, and image interpolation raises fundamental inquiries concerning the $C^{1}$ and higher-order regularity of $\infty$ -har…

math.AP2023

The boundedness of stable solutions to semilinear elliptic equations with linear lower bound on nonlinearities

Fa Peng

Let $2 \leq n \leq 9$ . Suppose that $f : R \to R$ is locally Lipschitz function satisfying $f (t) \geq A min {0, t} - K$ for all $t \in R$ with some constant $A \geq 0$ and $K \geq 0$ . We establish a…

math.AP2022★ 1 cited

Jacobian determinants for (nonlinear) gradient of planar $\infty$ -harmonic functions and applications

Hongjie Dong, Fa Peng, Yi Ru-Ya Zhang +1

In dimension 2, we introduce a distributional Jacobian determinant $det D V_{β} (D v)$ for the nonlinear complex gradient $(x_{1}, x_{2}) \mapsto ∣ D v ∣^{β} (v_{x_{1}}, - v_{x_{2}})$ for any $β > - 1$ , wh…

math.AP2022

A global second order Sobolev regularity for $p$ -Laplacian type equations with variable coefficients in bounded domains

Qianyun Miao, Fa Peng, Yuan Zhou

Let $Ω \subset R^{n}$ be a bounded convex domain with $n \geq 2$ . Suppose that $A$ is uniformly elliptic and belongs to $W^{1, n}$ when $n \geq 3$ or $W^{1, q}$ for some $q > 2$ when $n = 2$ . Fo…

math.AP2022

Interior Hölder regularity for stable solutions to semilinear elliptic equations up to dimension 5

Fa Peng, Yi Ru-Ya Zhang, Yuan Zhou

Let $2 \leq n \leq 5$ . We establish an apriori interior Hölder regularity of $C^{2}$ -stable solutions to the semilinear equation $- Δ u = f (u)$ in any domain of $R^{n}$ for any nonlinearity $f…

math.AP2021

$H W_{loc}^{2, 2}$ -regularity for $p$ -harmonic functions in Heisenberg groups

Jiayin Liu, Fa Peng, Yuan Zhou

Let $1 < p \leq 4$ when $n = 1$ and $1 < p < 3 + \frac{1}{n - 1}$ when $n \geq 2$ . We obtain the second-order horizontal Sobolev $H W_{loc}^{2, 2}$ -regularity of $p$ -harmonic functions in the H…

math.AP2021★ 4 cited

Optimal regularity & Liouville property for stable solutions to semilinear elliptic equations in $R^{n}$ with $n \geq 10$

Fa Peng, Yi Ru-Ya Zhang, Yuan Zhou

Let $0 \leq f \in C^{0, 1} (R^{n})$ . Given a domain $Ω \subset R^{n}$ , we prove that any stable solution to the equation $- Δ u = f (u)$ in $Ω$ satisfies a BMO interior regularit…

math.AP2019★ 3 cited

Regularity of absolute minimizers for continuous convex Hamiltonians

Peng Fa, Changyou Wang, Yuan Zhou

For any $n \geq 2$ , $Ω\subset\rn$, and any given convex and coercive Hamiltonian function $H\in C^{0}(\rn)$, we find an optimal sufficient condition on $H$ , that is, for any $c\in\ma…

The Lp Neumann problem for the Stokes system in nonsmooth domains

Maximal Sobolev regularity of the stress tensor for the symmetric gradient p-Laplace system

Regularity of stable radial solutions to semilinear elliptic equations in MEMS problems

A nonlinear Calderón-Zygmund L2-theory for the Dirichlet problem involving −∣Du∣γΔpN​u=f

Regularity from p-harmonic potentials to ∞-harmonic potentials in convex rings

The boundedness of stable solutions to semilinear elliptic equations with linear lower bound on nonlinearities

Jacobian determinants for (nonlinear) gradient of planar ∞-harmonic functions and applications

A global second order Sobolev regularity for p-Laplacian type equations with variable coefficients in bounded domains

Interior Hölder regularity for stable solutions to semilinear elliptic equations up to dimension 5

HWloc2,2​-regularity for p-harmonic functions in Heisenberg groups

Optimal regularity & Liouville property for stable solutions to semilinear elliptic equations in Rn with n≥10

Regularity of absolute minimizers for continuous convex Hamiltonians

The $L^{p}$ Neumann problem for the Stokes system in nonsmooth domains

A nonlinear Calderón-Zygmund $L^{2}$ -theory for the Dirichlet problem involving $- ∣ D u ∣^{γ} Δ_{p}^{N} u = f$

Regularity from $p$ -harmonic potentials to $\infty$ -harmonic potentials in convex rings

Jacobian determinants for (nonlinear) gradient of planar $\infty$ -harmonic functions and applications

A global second order Sobolev regularity for $p$ -Laplacian type equations with variable coefficients in bounded domains

$H W_{loc}^{2, 2}$ -regularity for $p$ -harmonic functions in Heisenberg groups

Optimal regularity & Liouville property for stable solutions to semilinear elliptic equations in $R^{n}$ with $n \geq 10$