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Characterization Of Domains Through Families Of Measures by Lucio R. Berrone is a Mathematics article available to read on EtoBox.

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Let Q be a plane domain limited by a regular Jordan curve F. For every (L) measurable subset E of T and every point z € CI, consider the probability P{E\ z) that a Brownian particle starting its motion at z hits the boundary T (by the first time) in a point belonging to E. Now, let C be a constant such that 0 < C < |T| and consider the optimization problem (1) sup{P(£;z):|£| = C} (| • | denotes the Lebesgue measure on the boundary T). What are the domains Q such that single arcs of the boundary are optimal subsets for (1) for every z 6 fi and every o<c< in? For a plane domain Cl which is starlike with respect to an interior point O, the internal visual angle ©(O; E) of a measurable subset of the boundary E C <90 is defined to be the single under which E is observed from O. Posing the optimization problem (2) sup{©(0;E):|E| = C}, it is asked for the convex domains CI such that single arcs of the boundary are optimal subsets for (2) for every O € CI and every 0 < C < |T|. A suitable response to these questions is given in this paper.

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Author

Lucio R. Berrone

Publisher

Walter de Gruyter GmbH

Published

2003

Language

EN

Field

Mathematics (Physical Sciences)