We present the state-of-the-art concerning the relativistic constraints, which describe the
geometry of hypersurfaces in a spacetime subject to the Einstein field equations. We review …

This book offers a systematic exposition of conformal methods and how they can be used to
study the global properties of solutions to the equations of Einstein's theory of gravity. It …

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Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

In this article, we re-examine some of the classical pointwise multiplication theorems in
Sobolev–Slobodeckij spaces, in part motivated by a simple counter-example that illustrates …

The purpose of this paper is to show well-posedness results for Dirichlet problems for the
Stokes and Navier–Stokes systems with L^ ∞ L∞-variable coefficients in L^ 2 L 2-based …

Let (M, g) be a compact Riemannian manifold on which a trace-free and divergence-free σ∈
W 1, p and a positive function τ∈ W 1, p, p> n are fixed. In this paper, we study the vacuum …

We prove the stability of the Einstein-scalar field Lichnerowicz equation under subcritical
perturbations of the critical nonlinearity in dimensions n= 3, 4, 5 n= 3, 4, 5. As a …

One of the most effective ways of constructing and studying solutions of Einstein's
gravitational field equations is via the Initial Value Problem. According to this approach, one …

In this note we prove two existence theorems for the Einstein constraint equations on
asymptotically Euclidean manifolds. The first is for arbitrary mean curvature functions with …

The purpose of this paper is to study boundary value problems of transmission type for the
Navier–Stokes and Darcy–Forchheimer–Brinkman systems in two complementary Lipschitz …