有界平滑區域上擬線性橢圓型問題強解的存在性

Abstract

我們討論下列在三維（含）以上空間有界平滑區域Z上之擬線性橢圓方程:Lu=f;針對u的二次微分項係數， 尋找適當的振當範圍以建立在 上之W(2,p) 全局估算。並藉由此估算，證明了此方程式具有屬於W(2,p)交集W(1,p) 之強解。

We consider quasilinear elliptic problems in a bounded smooth domain Z (dimZ=N). If the oscillations of a{ij}=a{ij}(x,r) with respect to r are sufficiently small, then a global W(2,p) estimate for a solution u is established and the existence of a strong solutionu u is proved.