Abstract
AbstractWe study spectral stability of the $${\bar{\partial }}$$
∂
¯
-Neumann Laplacian on a bounded domain in $${\mathbb {C}}^n$$
C
n
when the underlying domain is perturbed. In particular, we establish upper semi-continuity properties for the variational eigenvalues of the $${\bar{\partial }}$$
∂
¯
-Neumann Laplacian on bounded pseudoconvex domains in $${\mathbb {C}}^n$$
C
n
, lower semi-continuity properties on pseudoconvex domains that satisfy property (P), and quantitative estimates on smooth bounded pseudoconvex domains of finite D’Angelo type in $${\mathbb {C}}^n$$
C
n
.
Funder
National Science Foundatio
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Boas, H., Straube, E.: Global regularity for the $${{{\overline{\partial }}}}$$-Neumann problem: a survey of the $$L^2$$-Sobolev theory. In: Schneider, M., Siu, Y.-T. (eds.) Several Complex Variables, vol. 37, pp. 79–112. MSRI Publications, Berkeley (1999)
2. Brezis, H., Marcus, M.: Hardy’s inequalities revisited. Ann. Scuola Normale Super. Pisa-Classe Sci. 4(25), 217–237 (1997)
3. Burenkov, V., Lamberti, P.: Spectral stability of general non-negative self-adjoint operators with applications to Neumann-type operators. J. Differ. Equ. 233, 345–379 (2007)
4. Catlin, D.: Necessary conditions for subellipticity of the $${\overline{\partial }}$$-Neumann problem. Ann. Math. 117, 147–171 (1983)
5. Catlin, D.: Global regularity of the $${\overline{\partial }}$$-Neumann problem, Complex Analysis of Several Variables. In: Yum-Tong, S. (ed.), Proc. of Symp. in Pure Math. no. 41, Ameri. Math. Soc., pp. 39–49 (1984)
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