ANISOTROPIC SINGULARITY OF SOLUTIONS TO ELLIPTIC EQUATIONS IN A MEASURE FRAMEWORK

作者：Wang, Wanwan^*; Chen, Huyuan; Wang, Jian

来源：Electronic Journal of Differential Equations, 2015, 230.

• Anisotropy singularity
• weak solution
• uniqueness

In this article we study the weak solutions of elliptic equation
-Delta u = 2 partial derivative delta 0/partial derivative nu in Omega, u = 0 on partial derivative Omega
where Omega is an open bounded C-2 domain of R-N with N >= 2 containing the origin, v is a unit vector and (partial derivative delta 0)(partial derivative nu) is defined in the distribution sense, i.e.
= partial derivative zeta(0)/partial derivative nu, for all zeta is an element of C-0(1)(Omega).
We prove that this problem admits a unique weak solution u in the sense that
integral(Omega)u(-Delta)xi dx = 2 partial derivative xi(0)/partial derivative nu, for all xi is an element of C-0(2)(Omega).
Moreover, u has an anisotropic singularity and can be approximated, as t -> 0(+), by the solutions of
-Delta u = delta 1t nu - delta t nu/t in Omega, u = 0 on partial derivative Omega.

• 出版日期2015-9-10
• 单位江西师范大学