논문KCI 등재
GLOBAL SOLUTIONS FOR THE a-PROBLEM ON NON PSEUDOCONVEX DOMAINS IN STEIN MANIFOLDS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper, we prove basic a priori estimate for the $\overline\partial$-Neumann problem on an annulus between two pseudoconvex submanifolds of a Stein manifold. As a corollary of the result, we obtain the global regularity for the $\overline\partial$-problem on the annulus. This is a manifold version of the previous results on pseudoconvex domains.
Abstract
In this paper, we prove basic a priori estimate for the $\overline\partial$-Neumann problem on an annulus between two pseudoconvex submanifolds of a Stein manifold. As a corollary of the result, we obtain the global regularity for the $\overline\partial$-problem on the annulus. This is a manifold version of the previous results on pseudoconvex domains.
참고문헌 (14)
- H. Ahn, "Global boundary regularity for the ⎺∂-equation on q-pseudoconvex domains", Math. Nachr, 280(4), pp.343~350 (2007)
- H. Ahn, "Global regularity of ⎺∂ on an annulus between a Q-pseudoconvex and a P-pseudoconcave boundary", Pure Appl. Math. Q, 6(3), pp.647~661 (2010)
- S.-C. Chen, "Partial Differential Equations in Several Complex Vari-ables" (2001), Amer. Math. Soc
- H. R. Cho, "Global regularity of the ⎺∂-Neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (P)", Manuscripta Math, 90(4), pp.437~448 (1996)
- M. Dirridj, "Subelliptic estimate for the d-Neumann problem", Duke Math. J, 48(1), pp.93~107 (1981)
- G. B. Folland, "The Neumann problem for the Cauchy-Riemann complex" (1972), Princeton University Press
- L. Hormander, "L2 estimates and existence theorems for the ⎺∂ operator", Acta Math, 113, pp.89~152 (1965)
- S. Khidr, "Global regularity and Lp estimate for ⎺∂ on an annulus between two strictly pseudoconvex domains in a Stein manifold", C. R. Math. Acad. Sci. Paris, 351(23-24), pp.883~888 (2013)
- J. J. Kohn, "Global regularity for ⎺∂ on weakly pseudo-convex manifolds", Trans. Amer. Math. Soc, 181, pp.273~292 (1973)
- S. Saber, "The ⎺∂-problem on q-pseudoconvex domains with applications", Math. Slovaca, 63(3), pp.521~530 (2013)
- S. Saber, "Global regularity for ⎺∂ on an annulus between two weakly convex domains which satisfy property (P)", ~
- M.-C. Shaw, "Global solvability and regularity for ⎺∂ on an annulus between two weakly pseudoconvex domains", Trans. Amer. Math. Soc, 291(1), pp.255~267 (1985)
- M.-C. Shaw, "Complex analysis. Trends Math", pp.2010, Birkhuser
- E. J. Straube, "Lectures on the L2-Sobolev Theory of the ⎺∂-Neumann Problem", ESI Lectures in Mathematics and Physics, ~ (2010)
관련 논문AI추천
Solution to $\overline{\partial}$-problem with support conditions in weakly $q$-convex domainsSayed Saber대한수학회 · 대한수학회논문집2018 · 제33권 제2호The $\overline\partial$-problem with support conditions and pseudoconvexity of general order in K\"ahler manifoldsSayed Saber대한수학회 · 대한수학회지2016 · 제53권 제6호Explicit Sobolev estimates for the Cauchy-Riemann equation on parameters조상현, 최재서대한수학회 · 대한수학회보2008 · 제45권 제2호Stability of the dibar-estimates and the Mergelyan property for weakly q-convex manifolds서연숙영남수학회 · East Asian Mathematical Journal2008 · 제24권 제3호Sobolev estimates for the local extension of boundary holomorphic forms on real hypersurfaces in Cn조상현대한수학회 · 대한수학회지2013 · 제50권 제3호A bound on H\"older regularity for $\overline \partial$-equation on pseudoconvex domains in $\mathbb C^n$ with some comparable eigenvalues of the Levi-form조상현대한수학회 · 대한수학회보2021 · 제58권 제3호
이 간행물의 다른 논문 (13건)
INTEGRAL MEANS AND MAXIMUM AREA INTEGRAL PROBLEMS FOR CERTAIN FAMILY OF p-VALENT FUNCTIONSNavneet Lal Sharmapp. 1641-1665HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X8+A*X-tA = QMahmoud Mohseni Moghadam, Abbas Salemi, Mohsen Masoudipp. 1667-1682THE EXTREMAL PROBLEM ON HUA DOMAINSujuan Longpp. 1683-1698CLOSURE OPERATIONS AND THE DESCENDING CHAIN CONDITIONJanet C. Vassilevpp. 1699-1731GRADED INTEGRAL DOMAINS AND PRUFER-LIKE DOMAINS장규환pp. 1733-1757