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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…
math.AP2017★ 2 cited
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…
math.AP2013
A mean value formula of sub-p-Laplace parabolic equations on the Heisenberg group
Hairong Liu, Xiaoping Yang
We derive two equivalent definitions of the viscosity solutions to the homogeneous sub-p- Laplace parabolic equations on the Heisenberg group, and characterize the viscosity soluti…