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Capacity theory for monotone operators

TitleCapacity theory for monotone operators
Publication TypeJournal Article
Year of Publication1997
AuthorsDal Maso, G, Skrypnik, IV
JournalPotential Anal. 7 (1997), no. 4, 765-803

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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