112 citations · 304 across the 15 of their papers we have counts for
16 papers
A Scaling Approach to Elliptic Theory for Geometrically-Natural Differential Operators with Sobolev-Type Coefficients
Michael Holst, David Maxwell, Gantumur Tsogtgerel
We develop local elliptic regularity for operators having coefficients in a range of Sobolev-type function spaces (Bessel potential, Sobolev-Slobodeckij, Triebel-Lizorkin, Besov) w…
Sobolev-class asymptotically hyperbolic manifolds and the Yamabe problem
Paul T. Allen, John M. Lee, David Maxwell
We consider asymptotically hyperbolic manifolds whose metrics have Sobolev-class regularity, and introduce several technical tools for studying PDEs on such manifolds. Our results…
A Phase Space Approach to the Conformal Construction of Non-Vacuum Initial Data Sets in General Relativity
James Isenberg, David Maxwell
We present a uniform (and unambiguous) procedure for scaling the matter fields in implementing the conformal method to parameterize and construct solutions of Einstein constraint e…
Conformal Fields and the Structure of the Space of Solutions of the Einstein Constraint Equations
Mike Holst, David Maxwell, Rafe Mazzeo
The drift method, introduced by the second author, provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geome…
Numerical Bifurcation Analysis of the Conformal Method
James Dilts, Michael Holst, Tamara Kozareva +1
The conformal formulation of the Einstein constraint equations has been studied intensively since the modern version of the conformal method was first pub- lished in the early 1970…
Yamabe Classification and Prescribed Scalar Curvature in the Asymptotically Euclidean Setting
David Maxwell, James Dilts
We prove a necessary and sufficient condition for an asymptotically Euclidean manifold to be conformally related to one with specified nonpositive scalar curvature: the zero set of…