Abstract
The aim of this paper is to give a sufficient condition for existence and compactness of the \({\overline{\partial}}\) -Neumann operator N q on \({L^2_{(0,q)}(\Omega)}\) in the case Ω is an arbitrary q-convex domain in \({\mathbb{C}^n}\).
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Ahn H., Dieu N.Q.: The Donnelly–Fefferman theorem on q-pseudoconvex domains. Osaka J. Math. 46, 599–610 (2009)
Catlin, D.W.: Global regularity of the \({\overline{\partial}}\) -Neumann problem. In: Complex Analysis of Several Variables (Madison, 1982). Proceedings Symposia in Pure Mathematics, 41, pp. 39–49 (1984)
Chen S.C., Shaw, M.C.: Partial Differential Equations in Several Complex Variables, Studied in Advanced Mathematics, vol. 19. American Mathematical Society, Providence, RI (2001)
Demailly, J.: Complex analytic and differential geometry. http://www-fourier.ujf-grenoble.fr/demailly/manuscripts/agbook.pdf
Gansberger, K.: On the weighted \({\overline{\partial}}\) -Neumann problem on unbounded domains. arXiv:0912.0841
Gansberger, K., Haslinger, F.: Compactness estimates for the \({\overline{\partial}}\) -Neumann problem in weighted L 2-spaces on \({\mathbb{C}^n}\), to appear in Proccedings of the Conference on Complex Analysis 2008, in honour of Linda Rothschild. arXiv:0903.1783
Hai L.M., Dieu N.Q., Hong N.X.: L 2-Approximation of differential forms by \({\overline{\partial}}\) -closed ones on smooth hypersurfaces. J. Math. Anal. Appl. 383, 379–390 (2011)
Ho L.H.: \({\overline\partial}\) -Problem on weakly q-convex domains. Math. Ann. 290, 3–18 (1991)
Sibony N.: Une classes des domaines pseudoconvexe. Duke Math. J. 55, 299–319 (1987)
Straube E.J.: Plurisubharmonic functions and subellipticity of the \({\overline{\partial}}\) -Neumann problem on non-smooth domains. Math. Res. Lett. 4, 459–467 (1997)
Straube, E.J.: Lectures on the L 2-Sobolev theory of the \({\overline{\partial}}\) -Neumann problem. In: ESI Lectures in Mathematics and Physics. European Mathematical Society, Zürich (2010)
Walsh J.: Continuity of envelopes of plurisubharmonic functions. J. Math. Mech. 18, 143–148 (1968)
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Le, M.H., Nguyen, Q.D. & Nguyen, X.H. Existence and compactness for the \({\overline{\partial}}\) -Neumann operator on q-convex domains. manuscripta math. 144, 517–534 (2014). https://doi.org/10.1007/s00229-014-0661-2
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DOI: https://doi.org/10.1007/s00229-014-0661-2