Elliptic systems in H(s,delta) spaces on manifolds which are Euclidean at infinity

DOI10.1007/BF02392460zbMath0484.58028OpenAlexW2035743407MaRDI QIDQ1163776

Demetrios Christodoulou, Yvonne Choquet-Bruhat

Publication date: 1981

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02392460

zbMATH Keywords

closed range tensor bundle elliptic differential systems of order m on non-compact manifolds which are euclidean at infinity in weighted Sobolev spaces finite kernel and isomorphism theorems

Mathematics Subject Classification ID

Lua error in Module:PublicationMSCList at line 37: attempt to index local 'msc_result' (a nil value).

Related Items (only showing first 100 items - show all)

Dirac's observables for the rest-frame instant form of tetrad gravity in a completely fixed 3-orthogonal gauge ⋮ The general relativistic constraint equations ⋮ Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in $3+1$ dimensions ⋮ A note on mass-minimising extensions ⋮ Mathematical general relativity: A sampler ⋮ Vortices on asymptotically Euclidean Riemann surfaces ⋮ Solution of Nester’s gauge conditions ⋮ Integral operators determined by quasielliptic equations. I ⋮ Geodesics and the Einstein nonlinear wave system ⋮ Weak solutions of the Stokes problem in weighted Sobolev spaces ⋮ Complex powers on noncompact manifolds and manifolds with singularities ⋮ Post-Newtonian expansions for perfect fluids ⋮ Global existence of low regularity solutions of nonlinear wave equations ⋮ Existence of solutions of the Robinson-Trautman equation and spatial infinity ⋮ Dirichlet and Neumann exterior problems for the $n$-dimensional Laplace operator. An approach in weighted Sobolev spaces ⋮ Momenta and reduction for general relativity ⋮ Quasielliptic Operators and Equations Not Solvable with Respect to the Higher Order Derivative ⋮ Inverted finite elements: a new method for solving elliptic problems in unbounded domains ⋮ Total energy momentum in general relativity ⋮ Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds ⋮ Einstein-type elliptic systems ⋮ An extension procedure for the constraint equations ⋮ On existence and behaviour of asymptotically flat solutions to the stationary Einstein equations ⋮ Special orthonormal frames ⋮ The initial value problem for a class of general relativistic fluid bodies ⋮ Target patterns in a 2D array of oscillators with nonlocal coupling ⋮ Matrix quasi-elliptic operators in $\mathbb R^n$ ⋮ The helmhotz decomposition of weighted l^r-Spaces ⋮ Fourier transform is an isometry on some weighted Sobolev spaces ⋮ Local existence of solutions to the Euler-Poisson system, including densities without compact support ⋮ Isomorphism theorems for elliptic operators in Rⁿ ⋮ Unnamed Item ⋮ Dain’s invariant for black hole initial data ⋮ Local linearization stability ⋮ Long time existence from interior gluing ⋮ Vortices on surfaces with cylindrical ends ⋮ Hyperbolic methods for Einstein's equations ⋮ The Yamabe problem ⋮ Nonnegativity and well-posedness of the regular solution of the magnetized Boltzmann equation ⋮ The existence of a class of cosmic string solutions with infinite energy ⋮ On wave propagation in the Anti-de Sitter cosmology ⋮ Small deformations of extreme five dimensional Myers-Perry black hole initial data ⋮ Mapping Properties of One Class of Quasielliptic Operators ⋮ Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes: the constraint equations ⋮ The Thin-Sandwich Problem in General Relativity ⋮ Positive gravitational energy in arbitrary dimensions ⋮ Local model for moduli space of affine vortices ⋮ The boost problem in general relativity ⋮ On the geodesic hypothesis in general relativity ⋮ The coupled Yang-Mills-Boltzmann system in Bianchi type I space-time ⋮ Perelman's $\lambda $-functional on manifolds with conical singularities ⋮ Structure of the space of solutions of Einstein’s equations: A new variables approach ⋮ On the existence of asymptotically flat initial data sets for space-times containing manifolds with ends ⋮ The Klein-Gordon equation in the anti-de Sitter cosmology ⋮ The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. I. Local existence and smoothness properties ⋮ A relation between local and total energy in general relativity ⋮ On solvability of one class of quasielliptic systems ⋮ On the well-posedness of the vacuum Einstein's equations ⋮ Fredholm and regularity theory of Douglis-Nirenberg elliptic systems on ${\mathbb{R}}^{N}$ ⋮ Elliptic equations in weighted Besov spaces on asymptotically flat Riemannian manifolds ⋮ The Pohozaev-Schoen identity on asymptotically Euclidean manifolds: conservation laws and their applications ⋮ Smooth Compactly Supported Solutions of Some Underdetermined Elliptic PDE, with Gluing Applications ⋮ Remarks on the linking theory of shape dynamics ⋮ The Newtonian limit for perfect fluids ⋮ A gauge condition for orthonormal three-frames ⋮ Perturbative solutions of the extended constraint equations in general relativity ⋮ There are no<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>×<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">S</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>vacuum gravitational instantons ⋮ Numerical investigations of the asymptotics of solutions to the evolutionary form of the constraints ⋮ Continuity of the flow map for symmetric hyperbolic systems and its application to the Euler-Poisson system ⋮ A singular initial-boundary value problem for nonlinear wave equations and holography in asymptotically anti-de Sitter spaces ⋮ An equivalence theorem for string solutions of the Einstein matter-gauge equations ⋮ Yamabe numbers and the Brill-Cantor criterion ⋮ Some potentials for the curvature tensor on three-dimensional manifolds ⋮ Vacuum handles carrying angular momentum; electrovac handles carrying net charge ⋮ Solutions of the Einstein constraint equations with apparent horizon boundaries ⋮ Manifold structures for sets of solutions of the general relativistic constraint equations ⋮ The poisson equation with weights in exterior domains of Rⁿ ⋮ Geometric structure on the orbit space of gauge connections ⋮ The rest-frame instant form of metric gravity. ⋮ Weighted decay estimates for the wave equation ⋮ Global solution for massive Maxwell-Klein-Gordon equations with large Maxwell field ⋮ Rest frame system for asymptotically flat space–times ⋮ Reduced thin-sandwich equations on manifolds Euclidean at infinity and on closed manifolds: Existence and multiplicity ⋮ Unnamed Item ⋮ The Hilbert manifold of asymptotically flat metric extensions ⋮ Unnamed Item ⋮ Exterior stokes problems and decay at infinity ⋮ Unnamed Item ⋮ On quasielliptic operators in $\mathbb{R}_n$ ⋮ On the symplectic structure of general relativity ⋮ Breakdown of smooth solutions of the three-dimensional Euler–Poisson system ⋮ Spatial asymptotics and equilibria of heat flow on $\mathbb{R}^d$ ⋮ Reconstruction of cracks in an inhomogeneous anisotropic medium using point sources ⋮ On Witten's proof of the positive energy theorem ⋮ On elliptic systems in $R^ n$ ⋮ Elliptic operators and the decomposition of tensor fields ⋮ Existence theorem for solutions of Witten’s equation and nonnegativity of total mass ⋮ Fréchet Algebra Techniques for Boundary Value Problems on Noncompact Manifolds: Fredholm Criteria and Functional Calculus via Spectral Invariance ⋮ The nonlinear stability of the trivial solution to the Maxwell-Born-Infeld system ⋮ Regular Solutions for the relativistic Boltzmann equation in Yang-Mills field

Cites Work

This page was built for publication: Elliptic systems in H(s,delta) spaces on manifolds which are Euclidean at infinity