The Heat Equation for the -Neumann Problem, I

DOI10.1080/03605308708820498zbMath0615.58033OpenAlexW2004469311MaRDI QIDQ4722892

Nancy K. Stanton, Richard W. Beals

Publication date: 1987

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308708820498

zbMATH Keywords

heat equation\({\bar \partial }\)-Neumann problem\({\bar \partial }\)-Laplaciantrace of the heat semigroup

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Heat equation (35K05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

\(L^ p\) and Lipschitz estimates for the \({\bar\partial}\)-equation and the \({\bar\partial}\)-Neumann problem, Estimates on kernels for the \({\bar \partial}\)-equation and the \({\bar \partial}\)-Neumann problem, Hearing the type of a domain in \(\mathbb C^2\) with the \(\bar{\partial}\)-Neumann Laplacian, Intrinsic connections for Levi metrics, A zeta function associated to the sub-Laplacian on the unit sphere in \(\mathbb{C}^N\)

Cites Work

• Spectral geometry of singular Riemannian spaces
• The heat equation on a CR manifold
• Regular singular asymptotics
• The heat equation for the d-Neumann problem in a strictly pseudoconvex Siegel domain
• Spectral asymptotics for the delta-Neumann problem
• The fundamental solution of the heat equation associated with the \(\overline\partial\)-Neumann problem
• On integral representations and a priori Lipschitz estimates for the canonical solution of the \(\partial\)-equation
• Curvature and the eigenvalues of the Laplacian
• An asymptotic expansion for the heat equation
• Some Further Classes of Pseudo-Differential and Singular-Integral Operators Arising in Boundary-Value Problems I Composition of Operators
• Singular asymptotics approach to partial differential equations with isolated singularities in the coefficients
• Can One Hear the Shape of a Drum?
• Analytic Extension of the Trace Associated with Elliptic Boundary Problems