[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7468/jksmeb.2016.23.1.13

ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE

CHO, SUNGWON (DEPARTMENT OF MATHEMATICS EDUCATION, GWANGJU NATIONAL UNIVERSITY OF EDUCATION)

Publication Information

The Pure and Applied Mathematics / v.23, no.1, 2016 , pp. 13-19 More about this Journal

Abstract

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.

Keywords

elliptic Dirichlet boundary value problems; unbounded domain; exterior measure condition; Liouville property;

Citations & Related Records

Reference

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