Displaying similar documents to “Around the bounded L 2 curvature conjecture in general relativity”

Regularity and geometric properties of solutions of the Einstein-Vacuum equations

Sergiu Klainerman, Igor Rodnianski (2002)

Journées équations aux dérivées partielles

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We review recent results concerning the study of rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. We develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure...

Global existence for a quasilinear wave equation outside of star-shaped domains

Hart F. Smith (2001)

Journées équations aux dérivées partielles

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This talk describes joint work with Chris Sogge and Markus Keel, in which we establish a global existence theorem for null-type quasilinear wave equations in three space dimensions, where we impose Dirichlet conditions on a smooth, compact star-shaped obstacle 𝒦 ⊂ ℝ 3 . The key tool, following Christodoulou [1], is to use the Penrose compactification of Minkowski space. In the case under consideration, this reduces matters to a local existence theorem for a singular obstacle problem. Full details...

Dispersive and Strichartz estimates for the wave equation in domains with boundary

Oana Ivanovici (2010)

Journées Équations aux dérivées partielles

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In this note we consider a strictly convex domain Ω ⊂ ℝ d of dimension d ≥ 2 with smooth boundary ∂ Ω ≠ ∅ and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the dispersive estimates.