Interior estimates in sup-norm for generalized potential vectors

Author： Cuong Le  

Publisher： Taylor & Francis Ltd

ISSN： 1747-6933

Source： Complex Variables and Elliptic Equations, Vol.58, Iss.6, 2013-06, pp. : 813-820

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Abstract

The initial value problem of the type can be solved by contraction mapping principle in the case that the initial function Φ belongs to an associated space, whose elements satisfy an interior estimate. This article proves such interior estimate in the sup-norm for the generalized potential vectors. This proof is based on representation of generalized potential vectors by potential vectors. In that way this article is another example for the technique of transforming solutions of simpler partial differential equations into solutions of more general ones (see H. Begehr and R. P. Gilbert [4]).

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