Qian Zhang

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6 papers · 1 filter

math.AP2023★ 1 cited

Existence and asymptotics of normalized solutions for logarithmic Schrödinger system

Qian Zhang, Wenming Zou

This paper is concerned with the following logarithmic Schrödinger system: $$\left\{\begin{align} \ &\ -Δu_1+ω_1u_1=μ_1 u_1\log u_1^2+\frac{2p}{p+q}|u_2|^{q}|u_1|^{p-2}u_1,\\ \ &\…

math.AP2018

Boundary Hölder gradient estimates for the Monge-Ampère equation

Ovidiu Savin, Qian Zhang

We investigate global Hölder gradient estimates for solutions to the Monge-Ampère equation $det D^{2} u = f in Ω,$ where the right-hand side $f$ is bounded aw…

math.AP2018

Interior $C^{1, α}$ regularity on the linearized Monge-Amp $e ˋ$ re equation with $VMO$ type coefficients

Lin Tang, Qian Zhang

In this paper, we establish interior $C^{1, α}$ estimates for solutions of the linearized Monge-Amp $e ˋ$ re equation $L_{ϕ} u := tr [Φ D^{2} u] = f,$ where the densit…

math.AP2018

Global $W^{2, p}$ regularity on the linearized Monge-Amp $e ˋ$ re equation with $VMO$ type coefficients

Lin Tang, Qian Zhang

In this paper, we establish global $W^{2, p}$ estimates for solutions of the linearized Monge-Amp $e ˋ$ re equation $L_{ϕ} u := tr [Φ D^{2} u] = f,$ where the density…

math.AP2018

Global $C^{1 + α, \frac{1 + α}{2}}$ regularity on the linearized parabolic Monge-Amp $e ˋ$ re equation

Lin Tang, Qian Zhang

In this paper, we establish global $C^{1 + α, \frac{1 + α}{2}}$ estimates for solutions of the linearized parabolic Monge-Amp $e ˋ$ re equation $$\mathcal{L}_ϕu(x,t):=-u_t\,\mathrm{…

math.AP2018

Boundary regularity for Monge-Ampère equations with unbounded right hand side

Ovidiu Savin, Qian Zhang

We consider Monge-Ampère equations with right hand side $f$ that degenerate to $\infty$ near the boundary of a convex domain $Ω$ , which are of the type $$\mathrm{det}\;D^2 u=f\quad…

Existence and asymptotics of normalized solutions for logarithmic Schrödinger system

Boundary Hölder gradient estimates for the Monge-Ampère equation

Interior C1,α regularity on the linearized Monge-Ampeˋre equation with VMO type coefficients

Global W2,p regularity on the linearized Monge-Ampeˋre equation with VMO type coefficients

Global C1+α,21+α​ regularity on the linearized parabolic Monge-Ampeˋre equation

Boundary regularity for Monge-Ampère equations with unbounded right hand side

Interior $C^{1, α}$ regularity on the linearized Monge-Amp $e ˋ$ re equation with $VMO$ type coefficients

Global $W^{2, p}$ regularity on the linearized Monge-Amp $e ˋ$ re equation with $VMO$ type coefficients

Global $C^{1 + α, \frac{1 + α}{2}}$ regularity on the linearized parabolic Monge-Amp $e ˋ$ re equation