ﻻ يوجد ملخص باللغة العربية
In this note, we study Liouville type theorem for conformal Gaussian curvature equation (also called the mean field equation) $$ -Delta u=K(x)e^u, in R^2 $$ where $K(x)$ is a smooth function on $R^2$. When $K(x)=K(x_1)$ is a sign-changing smooth function in the real line $R$, we have a non-existence result for the finite total curvature solutions. When $K$ is monotone non-decreasing along every ray starting at origin, we can prove a non-existence result too. We use moving plane method and moving sphere method.
In this paper, we prove several Liouville type results for a nonlinear equation involving infinity Laplacian with gradient of the form $$Delta^gamma_infty u + q(x)cdot abla{u} | abla{u}|^{2-gamma} + f(x, u),=,0quad text{in}; mathbb{R}^d,$$ where $ga
In this paper, we derive a priori interior Hessian estimates for Lagrangian mean curvature equation if the Lagrangian phase is supercritical and has bounded second derivatives.
This note is devoted to investigating Liouville type properties of the two dimensional stationary incompressible Magnetohydrodynamics equations. More precisely, under smallness conditions only on the magnetic field, we show that there are no non-triv
We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space $R^n$, the hyperbolic space $H^n$ and a Riemannian manifold $mathfrak{S^n}$ ($ngeq 3$) with the Schwarzschild metric to any Riemannian manifold $N$.
In this paper, we solve the Dirichlet problem with continuous boundary data for the Lagrangian mean curvature equation on a uniformly convex, bounded domain in $mathbb{R}^n$.