Smooth Compactly Supported Solutions of Some Underdetermined Elliptic PDE, with Gluing Applications

DOI10.1080/03605302.2012.711794zbMath1268.58018arXiv1003.0535OpenAlexW2964137612MaRDI QIDQ4902746

Erwann Delay

Publication date: 17 January 2013

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

Full work available at URL: https://arxiv.org/abs/1003.0535

zbMATH Keywords

Riemannian manifoldgluingcompactly supported solutionsundetermined elliptic PDE

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) Elliptic equations on manifolds, general theory (58J05) PDEs in connection with relativity and gravitational theory (35Q75)

Related Items

Gluing construction of initial data with Kerr-de Sitter ends ⋮ Local well-posedness of the \((4 + 1)\)-dimensional Maxwell-Klein-Gordon equation at energy regularity ⋮ An extension procedure for the constraint equations ⋮ A TT tensor machine on Einstein manifolds ⋮ Local and global scalar curvature rigidity of Einstein manifolds ⋮ Inversion formulas and range characterizations for the attenuated geodesic ray transform ⋮ Recent progress in general relativity ⋮ Analysis, geometry and topology of positive scalar curvature metrics. Abstracts from the workshop held June 27 -- July 3, 2021 (hybrid meeting) ⋮ Black hole gluing in de Sitter space ⋮ A limit equation associated to the solvability of the vacuum Einstein constraint equations by using the conformal method ⋮ Initial data sets with ends of cylindrical type. I: The Lichnerowicz equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Construction of \(N\)-body initial data sets in general relativity
• Localized gluing of Riemannian metrics in interpolating their scalar curvature
• Harmonic metrics, harmonic tensors, and Gauss maps
• Gluing constructions for asymptotically hyperbolic manifolds with constant scalar curvature
• Asymptotically flat conformal structures
• The boost problem in general relativity
• Elliptic systems in H(s,delta) spaces on manifolds which are Euclidean at infinity
• Gluing and Wormholes for the Einstein constraint equations
• On the existence and stability of the Penrose compactification
• Interior regularity of solutions to the isotropically constrained Plateau problem
• Pseudo-differential operators and non-elliptic boundary problems
• Generalized Korn's inequality and conformal Killing vectors
• On the asymptotics for the vacuum Einstein constraint equations
• Some decompositions of the space of symmetric tensors on a Riemannian manifolds
• Bowen–York tensors
• Manifolds of Riemannian metrics with prescribed scalar curvature
• Constant mean curvature solutions of the Einstein constraint equations on closed manifolds
• Linearization stability of the Einstein constraint equations on an asymptotically hyperbolic manifold
• Non‐coercive boundary value problems
• Decomposition of Vector-Valued Divergence Free Sobolev Functions and Shape Optimization for Stationary Navier–Stokes Equations
• PROLONGATIONS OF GEOMETRIC OVERDETERMINED SYSTEMS
• Fredholm operators and Einstein metrics on conformally compact manifolds
• Extension and representation of divergence-free vector fields on bounded domains
• Scalar curvature deformation and a gluing construction for the Einstein constraint equations