拟线性椭圆型微分方程的相对弱解

Relative Weak Solution of Quasilinear Elliptic Partial Differential Equations of Second Order

利用相对Sobolev空间Wk0,p(Ω,Σ)的概念讨论不适定边界的二阶散度型拟线性椭圆型微分方程.首先给出了不适定边界二阶散度型拟线性椭圆型微分方程相对弱解的概念,化不适定问题为适定问题,进而讨论了与弱解的关系,并给出了相对弱下解的有界性估计.

The quasilinear elliptic partial differential equation of second order with Ill-posed boundary is discussed by using relative Sobolev space W0^k,p（Ω,Σ） . Besides, the relative weak so- lution of quasilinear elliptic partial differential equation is introduced, changing the ill-posed prob- lem to well-posed poblem, and the boundedness of relative weak solution is studied.