一类具退化强制的椭圆方程在加权Sobolev空间中重整化解的存在性

Existence of renormalized solutions for a degenerate elliptic equation with degenerate coercivity in weighted Sobolev spaces

运用截断方法研究了一类椭圆方程在加权Sobolev空间中解的存在性.主要采用Marcinkiewicz估计,在得到逼近解序列的截断函数先验估计的基础上,通过选取适当的检验函数,对逼近解序列做合适的估计,以此证明重整化解的存在性.

In this paper,we consider the following nonlinear elliptic equation with degenerate coercivity and lower order term in the setting of the weighted Sobolev space.We investigate the existence of the renormalized solutions in W 1,p 0(Ω,ω)by the truncation method.With the help of Marcinkiewicz estimate,through some priori estimates for the sequence of solutions of the approximate problem,we prove that u n converges in measure.Then we choose suitable test functions for the approximate equation and obtain the needed estimates.Finally,through a limit process,we obtain the existence of renormalized solutions to problem.