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ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE
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  • Journal title : The Pure and Applied Mathematics
  • Volume 23, Issue 1,  2016, pp.13-19
  • 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;
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 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;
 Language
English
 Cited by
 References
1.
H. Berestycki, L. Nirenberg & S.R.S. Varadahn: The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Comm. Pure Appl. Math. 47 (1994), 47-92 crossref(new window)

2.
X. Cabre: On the Alexandroff-Bekelman-Pucci estimate and reversed Hölder inequality for solutions of elliptic and parabolic equations. Comm. Pure Appl. Math. 48 (1995), 539-570. crossref(new window)

3.
V. Cafagna & A. Vitolo: On the maximum principle for second-order elliptic operators in unbounded domains. C. R. Acad. Sci. Paris. Ser. I 334 (2002), 1-5 crossref(new window)

4.
O.A. Ladyzhenskaya & N.N. Uraltseva: Linear and Quasilinear Elliptic Equations. Nauka, Moscow, 1964, English translation: Academic Press, New York, 1968; 2nd Russian ed. 1973.

5.
A. Vitolo: On the maximum principle for complete second-order elliptic operators in general domains. J. Diff. equations 194 (2003), no. 1, 166-184. crossref(new window)