Partial Differential Equations
Absolute continuity results for superdiffusions with applications to differential equations
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 605-610.

Let X=(XD,Pμ) be a superdiffusion in a domain E d . We introduce a germ σ-algebra E- at the boundary of E and we prove that, on this σ-algebra, Pμ1 is absolutely continuous with respect to Pμ2 if μ1 and μ2 are concentrated on compact subsets of E. In combination with previous results of Dynkin, Kuznetsov and Mselati, this leads to a complete classification of positive solutions of equation Δu=uα in a bounded domain E of class C4 for the case 1<α⩽2.

On établit un résultat qui, combiné à des travaux antérieurs de Dynkin, Kuznetsov et Mselati, conduit à une classification complète des solutions positives de l'équation Δu=uα dans un domaine borné régulier E, pour 1<α⩽2.

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Published online:
DOI: 10.1016/j.crma.2004.01.028
Dynkin, Eugene B. 1

1 Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
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Dynkin, Eugene B. Absolute continuity results for superdiffusions with applications to differential equations. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 605-610. doi : 10.1016/j.crma.2004.01.028. http://www.numdam.org/articles/10.1016/j.crma.2004.01.028/

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