Mathematical Research Letters

Volume 10 (2003)

Number 1

Poisson capacities

Pages: 85 – 95

DOI: http://dx.doi.org/10.4310/MRL.2003.v10.n1.a9

Authors

E. B. Dynkin (Cornell University)

S. E. Kuznetsov (University of Colorado, Boulder)

Abstract

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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