GOOD ELLIPTIC OPERATORS ON CANTOR SETS

Construction de mesures elliptiques absolument continues sur un ensemble de Cantor du plan. 18p/10dessins; It is well known that a purely unrectifiable set cannot support a harmonic measure which is absolutely continuous with respect to the Hausdorff measure of this set. We show that nonetheless there exist elliptic operators on (purely unrectifiable) Cantor sets in R 2 whose elliptic measure is absolutely continuous, and in fact, essentially proportional to the Hausdorff measure.