Mathematical Research Letters

Volume 10, Issue 1, January 2003 pp. 85-95.

Poisson capacities

Authors: E.B. Dynkin and S.E. Kuznetsov
Author institution: Cornell University, and University of Colorado, Boulder

Summary: Poisson capacities appeared, first, in the theory of removable boundary singularities for solutions of semilinear elliptic differential equations. It seems that these capacities should play a key role for solving the problem: to describe all positive solutions of the equation $Lu=u^\alpha$ with $\alpha>1$ in a smooth domain. We establish two inequalities for the Poisson capacities which might be useful for this task.

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