95-460 Arrieta, Jose M.
Elliptic Equations, Principal Eigenvalue and Dependence on the Domain. (69K, LaTeX) Oct 16, 95
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Abstract. We consider a general second order uniformly elliptic differential operator \$L\$ and also the set \$\Theta\$ of all open sets (not neccessarily smooth) in the unit ball of \$\R^n\$. We define a metric \$d\$ in this set (up to an equivalence relation \$\sim\$) that makes the space \$(\Theta/\sim, d)\$ a complete metric space. We show that the principal eigenvalue and eigenfunction of \$L\$ are continuous with the metric \$d\$. Similar results are obtained for the solutions of the equation \$Lv=f\$.

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