Shiguang Ma

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20242026

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math.AP2026

Gradient potential estimates for k-Hessian equations

Huajie Liu, Shiguang Ma, Shengyang Zang

For $2 \leq k < n$ , we prove pointwise gradient bounds for proper weak $k$ -convex functions in terms of a local average and a Wolff potential of the full Hessian measure $F_{k} [u]$ . The…

math.AP2026

Quasilinear Equations with Exponential Reactions and Measure Data on Carnot Groups

Shiguang Ma, Zijian Wang

In this paper, we establish existence and pointwise Wolff potential bounds for nonnegative solutions of $- Δ_{G, p} u = H_{l} (α u^{β}) + μ$ on Carnot groups, where $H_l(t)=e^t-\sum_{j…

math.AP2025

Isolated singularities of solutions of certain quasi-linear elliptic inequalities

Shiguang Ma, Shengyang Zang

We provide a complete classification of the asymptotic behavior of isolated singularities for solutions satisfying \[ 0\le-Δ_{p}u(x)\le τu^{\frac{n(p-1)}{n-p}} (x),\,\,u(x)\ge0,\,\…

math.AP2024

$N$ -Laplacian and $N /2$ -Hessian type equations with exponential reaction term and measure data

Shiguang Ma, Zijian Wang

In this article, we will prove existence results for the equations of the type $- Δ_{N} u = H_{l} (u) + μ$ and $F_{\frac{N}{2}} [- u] = H_{l} (u) + μ$ in a bounded domain $Ω$ , with Dirichlet bou…

Gradient potential estimates for k-Hessian equations

Quasilinear Equations with Exponential Reactions and Measure Data on Carnot Groups

Isolated singularities of solutions of certain quasi-linear elliptic inequalities

N -Laplacian and N/2-Hessian type equations with exponential reaction term and measure data

$N$ -Laplacian and $N /2$ -Hessian type equations with exponential reaction term and measure data