Elliptic Equations in Weighted Besov Spaces on Asymptotically Flat\n Riemannian Manifolds

2012/09/12 by Uwe Brauer, Brauer, Uwe, Lavi Karp +1
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1209.2642

openalex publication_date 2012/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the applications of weighted Besov spaces to elliptic\nequations on asymptotically flat Riemannian manifolds, and in particular to the\nsolutions of Einstein's constraints equations. We establish existence theorems\nfor the Hamiltonian an momentum constraints with constant mean curvature and\nwith a background metric which satisfies very low regularity assumptions. These\nresults extend the regularity results of Holst, Nagy and Tsogtgerel about the\nconstraint equations on compact manifolds in the Besov space B_p,p^s, to\nasymptotically flat manifolds. We also consider the Brill--Cantor criterion in\nthe weighted Besov spaces. Our results improve the regularity assumptions on\nasymptotically flat manifolds Choquet--Bruhat, Isenberg and Pollack, and\nMaxwell, as well as they enable us to construct the initial data for the\nEinstein--Euler system.\n

Citations

• On the proof of the positive mass conjecture in general relativity

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