4 papers
Symmetry in Serrin-type overdetermined problems
Daomin Cao, Juncheng Wei, Weicheng Zhan
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overd…
Desingularization of vortices for the incompressible Euler equation on a sphere
Daomin Cao, Shuanglong Li, Guodong Wang
In this paper, we construct a family of global solutions to the incompressible Euler equation on a standard 2-sphere. These solutions are odd-symmetric with respect to the equatori…
Expansion of Green's function and regularity of Robin's function for elliptic operators in divergence form
Daomin Cao, Jie Wan
We consider Green's function of the elliptic operator in divergence form on a bounded smooth domain $ Ω\subseteq\mathbb{R}^n (n\g…
Clustered helical vortices for 3D incompressible Euler equation in infinite cylinders
Daomin Cao, Jie Wan
In this article, we first consider solutions to a semilinear elliptic problem in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\va…