Publisher : Korea Society of Mathematical Education
DOI : 10.7468/jksmeb.2016.23.1.13
Title & Authors
ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE CHO, SUNGWON;
In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.
elliptic Dirichlet boundary value problems;unbounded domain;exterior measure condition;Liouville property;
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