Annales Academię Scientiarum Fennicę
Mathematica
Volumen 33, 2008, 413-427.

EQUALITY CASES IN THE SYMMETRIZATION INEQUALITIES FOR BROWNIAN TRANSITION FUNCTIONS AND DIRICHLET HEAT KERNELS

Dimitrios Betsakos

Aristotle University of Thessaloniki, Department of Mathematics
54124 Thessaloniki, Greece; betsakos 'at' math.auth.gr

Abstract. We prove equality statements for the symmetrization inequalities for Brownian transition functions and Dirichlet heat kernels. The proofs involve the equality statements for the related polarization inequalities which we also prove. These results lead to symmetrization inequalities for Green functions, condenser capacities, and exit times of Brownian motion.

2000 Mathematics Subject Classification: Primary 35K05, 35B05, 31B15, 60J65.

Key words: Heat kernel, polarization, symmetrization, transition probability, Brownian motion, capacity, Green function.

Reference to this article: D. Betsakos: Symmetrization inequalities for Brownian transition functions and Dirichlet heat kernels. Ann. Acad. Sci. Fenn. Math. 33 (2008), 413-427.

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