2 citations · 5 across the 11 of their papers we have counts for
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Critical points of solutions to a kind of linear elliptic equations in multiply connected domains
Haiyun Deng, Hairong Liu, Xiaoping Yang
In this paper, we mainly study the critical points and critical zero points of solutions to a kind of linear elliptic equations with nonhomogeneous Dirichlet boundary condition…
Interior C^{1,1} regularity of solutions to degenerate Monge-Ampère type equations
Feida Jiang, Juhua Shi, Xiaoping Yang
In this paper, we study the interior C^{1,1} regularity of viscosity solutions for a degenerate Monge-Ampère type equation \det[D^{2}u-A(x, u, Du)]=B(x, u, Du) when B \geq 0 and B^…
Upper Measure Bounds of Nodal Sets of Solutions to the Bi-Harmonic Equations on Riemannian Manifolds
Long Tian, Xiaoping Yang
In this paper, we consider the nodal set of a bi-harmonic function on an dimensional Riemannian manifold , that is, satisfies the equation $\triangle_M^…
Measure Upper Bounds of Nodal Sets of Robin Eigenfunctions
Fang Liu, Long Tian, Xiaoping Yang
In this paper, we obtain the upper bounds for the Hausdorff measures of nodal sets of eigenfunctions with the Robin boundary conditions, i.e., \begin{equation*} {\left\{\begin{arra…
Measure Upper Bounds for Nodal Sets of Eigenfunctions of the bi-Harmonic Operator
Long Tian, Xiaoping Yang
In this article, we consider eigenfunctions of the bi-harmonic operator, i.e., on with some homogeneous linear boundary conditions. We assume that $Ω\su…
Complex Monge-Ampère equations with oblique boundary value
Ni Xiang, Xiaoping Yang
The existence and regularity of the classical plurisubharmonic solution for complex Monge-Ampère equations subject to the semilinear oblique boundary condition which is C^1 perturb…