Capacity theory for monotone operators

G. Dal Maso; I. V. Skrypnik

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arXiv · funct-an/9501005

Capacity theory for monotone operators

G. Dal Maso·I. V. Skrypnik

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Abstract

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 $F$.

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G. Dal Maso, I. V. Skrypnik. 1995-01-19. Capacity theory for monotone operators. https://arxiv.org/abs/funct-an/9501005

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