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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A notion of capacity which characterizes removable singularities


Authors: Reese Harvey and John C. Polking
Journal: Trans. Amer. Math. Soc. 169 (1972), 183-195
MSC: Primary 35Q99; Secondary 31C15
MathSciNet review: 0306740
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Abstract: In this paper the authors define a capacity for a given linear partial differential operator acting on a Banach space of distributions. This notion has as special cases Newtonian capacity, analytic capacity, and AC capacity. It is shown that the sets of capacity zero are precisely those sets which are removable sets for the corresponding homogeneous equation. Simple properties of the capacity are derived and special cases examined.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0306740-4
PII: S 0002-9947(1972)0306740-4
Keywords: Partial differential operators, capacity, removable singularities, capacitary potential, capacitary mass
Article copyright: © Copyright 1972 American Mathematical Society