Extensions of Green Functions and the Representation of Greatest Thermic Minorants

New Zealand Journal of Mathematics (Online)

Neil A. Watson

关键词: Green function;    integral representation;    greatest thermic minorant.;   

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 摘 要 】

We prove a representation formula for the extended Green function of an open subset D of an open set E, in terms of the Green function of E. Using this result, we deduce a formula for the greatest thermic minorant on D of any heat potential on E, and of any supertemperature on E if the closure of D is a compact subset of E. In the latter case, we also determine a necessary and sufficient condition under which the greatest thermic minorant on D, of an arbitrary supertemperature v on E, is given by the Poisson integral of the restriction of v to .

【 授权许可】

Unknown