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ISSN : 1226-0657

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Vol.23 No.1
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ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE

ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.1, pp.13-19
https://doi.org/10.7468/jksmeb.2016.23.1.13
CHO, SUNGWON (DEPARTMENT OF MATHEMATICS EDUCATION, GWANGJU NATIONAL UNIVERSITY OF EDUCATION)
CHO, SUNGWON. (2016). ON SOME UNBOUNDED DOMAINS FOR A MAXIMUM PRINCIPLE. 한국수학교육학회지시리즈B:순수및응용수학, 23(1), 13-19, https://doi.org/10.7468/jksmeb.2016.23.1.13
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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

참고문헌

1.

Berestycki, H.;Nirenberg, L.;Varadahn, S.R.S.;. (1994). The principal eigenvalue and maximum principle for second-order elliptic operators in general domains. Comm. Pure Appl. Math., 47, 47-92. 10.1002/cpa.3160470105.

2.

Cabre, X.;. (1995). On the Alexandroff-Bekelman-Pucci estimate and reversed Hölder inequality for solutions of elliptic and parabolic equations. Comm. Pure Appl. Math., 48, 539-570. 10.1002/cpa.3160480504.

3.

Cafagna, V.;Vitolo, A.;. (2002). On the maximum principle for second-order elliptic operators in unbounded domains. C. R. Acad. Sci. Paris. Ser. I, 334, 1-5. 10.1016/S1631-073X(02)02204-5.

4.

Ladyzhenskaya, O.A.;Uraltseva, N.N.;. Linear and Quasilinear Elliptic Equations.

5.

Vitolo, A.;. (2003). On the maximum principle for complete second-order elliptic operators in general domains. J. Diff. equations, 194(1), 166-184. 10.1016/S0022-0396(03)00193-1.

한국수학교육학회지시리즈B:순수및응용수학

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