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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.
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참고문헌 (5)
참고문헌 신청
H. Berestycki / 1994 / The principal eigenvalue and maxi-mum principle for second-order elliptic operators in general domains / Comm. Pure Appl. Math 47:47~92
X. Cabre / 1995 / On the Alexandro®-Bekelman-Pucci estimate and reversed HÄolder inequality for solutions of elliptic and parabolic equations / Comm. Pure Appl. Math 48:539~570
V. Cafagna / 2002 / On the maximum principle for second-order elliptic operators in unbounded domains / C. R. Acad. Sci. Paris. Ser. I 334:1~5
O.A. Ladyzhenskaya / 1964 / Linear and Quasilinear Elliptic Equa-tions / Nauka
A. Vitolo / 2003 / On the maximum principle for complete second-order elliptic operators in general domains / J. Di®. equations 194(1):166~184
X. Cabre / 1995 / On the Alexandro®-Bekelman-Pucci estimate and reversed HÄolder inequality for solutions of elliptic and parabolic equations / Comm. Pure Appl. Math 48:539~570
V. Cafagna / 2002 / On the maximum principle for second-order elliptic operators in unbounded domains / C. R. Acad. Sci. Paris. Ser. I 334:1~5
O.A. Ladyzhenskaya / 1964 / Linear and Quasilinear Elliptic Equa-tions / Nauka
A. Vitolo / 2003 / On the maximum principle for complete second-order elliptic operators in general domains / J. Di®. equations 194(1):166~184
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