标题： 单调算子的容量理论 显示英文标题

标题： Capacity theory for monotone operators

摘要： 如果 $Au=-div(a(x,Du))$ 是在 Sobolev 空间 $W^{1,p}(R^n)$, $1<p<+\infty$上定义的单调算子，且对于几乎处处 $a(x,0)=0$ 成立 $x\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\subset F$. 我们证明$C_A(E,F)$关于$E$是递增且可数次可加的，关于$F$是递减的。 此外，我们研究了$C_A(E,F)$关于$E$和$F$的连续性性质。 显示英文摘要

摘要： If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1<p<+\infty$, with $a(x,0)=0$ for a.e. $x\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in $R^n$ with $E\subset F$. We prove that $C_A(E,F)$ is increasing and countably subadditive with respect to $E$ and decreasing with respect to $F$. Moreover we investigate the continuity properties of $C_A(E,F)$ with respect to $E$ and $F$.