Xi-nan Ma

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math.AP2026

Liouville Rigidity for Entire Strictly Spacelike Solutions of a Lorentzian Prescribed Mean Curvature Equation

Xi-Nan Ma, Tian Wu, Wangzhe Wu +1

We prove a Liouville theorem for nonnegative entire strictly spacelike solutions of \[ \operatorname{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right)+u^p=0 \qquad\text{in }\…

math.AP2024

Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in $R^{n}$

Xi-Nan Ma, Wangzhe Wu

We improve the Liouville theorem for the equation $- I^ v = v^{p} ∣\nabla v ∣^{q}$ in $R^{n}$ , which was studied by Bidaut-VÃ©ron, GarcÃa-Huidobro, and VÃ©ron. The proof is based o…

math.AP2024

Liouville theorem for elliptic equations involving the sum of the function and its gradient in $R^{n}$

Xi-Nan Ma, Wangzhe Wu, Qiqi Zhang

We prove Liouville theorem for the equation $I^ v + N v^{p} + M ∣\nabla v ∣^{q} = 0$ in $R^{n}$ , with $M, N > 0, q = \frac{2 p}{p + 1}$ in the critical and subcritical case. The pr…

math.AP2024

Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities

Daowen Lin, Xi-Nan Ma

We derive an integral identity for a class $p$ -Laplace equation, and then classify all positive finite energy cylindrically symmetric solutions of the equation (\ref{1.2}) for $3\l…

math.AP2024

$I ¨ _{k}$ -Yamabe measure

Xi-Nan Ma, Wangzhe Wu

We found a special divergence structure for the $I ¨ _{k}$ -Yamabe operator and use it to get a monotonicity formula. We also get an interior $L^{\infty}$ estimate via its $L^{1}$ norm fo…

Liouville Rigidity for Entire Strictly Spacelike Solutions of a Lorentzian Prescribed Mean Curvature Equation

Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in Rn

Liouville theorem for elliptic equations involving the sum of the function and its gradient in Rn

Best constant and extremal functions for a class Hardy-Sobolev-Maz'ya inequalities

I¨k​-Yamabe measure

Liouville theorem for elliptic equations with a source reaction term involving the product of the function and its gradient in $R^{n}$

Liouville theorem for elliptic equations involving the sum of the function and its gradient in $R^{n}$

$I ¨ _{k}$ -Yamabe measure