 95460 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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