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math.AP2018
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…
math.AP2018
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^…
math.AP2018
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…