We prove the existence of a maximum principle for operators of the type , for weights with subharmonic. It is associated with certain simply connected subdomains that are produced by a Hele-Shaw flow emanating from a given point in the domain. For constant weight, these are the circular disks in the domain. The principle is equivalent to the following statement. THEOREM. Suppose is logarithmically subharmonic on the unit disk, and that the weight times area measure is a reproducing measure (for the harmonic functions). Then the Green function for the Dirichlet problem associated with on the unit disk is positive.
@article{JEDP_1999____A3_0,
author = {Hedenmalm, H\aa kan},
title = {An Hadamard maximum principle for the biplacian on hyperbolic manifolds},
journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
year = {1999},
pages = {1-5},
mrnumber = {1718958},
language = {en},
url = {http://dml.mathdoc.fr/item/JEDP_1999____A3_0}
}
Hedenmalm, Håkan. An Hadamard maximum principle for the biplacian on hyperbolic manifolds. Journées équations aux dérivées partielles, (1999), pp. 1-5. http://gdmltest.u-ga.fr/item/JEDP_1999____A3_0/
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