擬線性橢圓方程式強解之存在性

Abstract

對於N 維空間, 有界的定義域上, 給于一個擬線性橢圓方程式 Lu+g=0, g 是一個 Caratheodory 函數, 滿足 quadratic生長條件, 若改變g 的條 件, 使吾人不僅可獲得其弱解, 更進一步獲得其強解. We study the quasilinear elliptic problem Lu+g(x,u,.gradient. u)=0 on a regular bound domain .OMEGA., g is a Caratheodory function satisfying quadratic growth condition. If we change growth condition of g, not only we can get the weak solution of the problem ,but the strong solution.