论文标题
一些强烈退化二阶椭圆方程的多个解决方案
Multiple solutions for some strongly degenerate second order elliptic equations
论文作者
论文摘要
我们考虑在一个有限域中的边界价值问题，涉及$$ l（u）= - \ textrm {div}（a（x）\ nabla u）$$和合适的非线性$ f $的简并运算符。该函数$ a $在平滑的1次辅助子手机上的$ω$中消失，而不允许它为$ c^{2} $。通过使用加权Sobolev空间，我们仍然能够找到解决方案的存在，这些解决方案在痕量意义上消失了，$ a $ a $消失。
We consider a boundary value problem in a bounded domain involving a degenerate operator of the form $$L(u)=-\textrm{div} (a(x)\nabla u)$$ and a suitable nonlinearity $f$. The function $a$ vanishes on smooth 1-codimensional submanifolds of $Ω$ where it is not allowed to be $C^{2}$. By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where $a$ vanishes.
