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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