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

Oana Ivanovici

Type: Article

Publication Date: 2010-12-14

Citations: 1

DOI: https://doi.org/10.5802/jedp.68

Abstract

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.

Locations

Journées Équations aux dérivées partielles - View - PDF
French digital mathematics library (Numdam) - View - PDF

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+	Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III	2001	Daniel Tataru
+	Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations	1977	Robert S. Strichartz
+	Counter-examples to the Strichartz estimates for the wave equation in domains II	2009	Oana Ivanovici
+	Global existence for energy critical waves in 3-d domains	2008	Nicolas Burq Gilles Lebeau Fabrice Planchon
+ PDF Chat	A parametrix construction for wave equations with $C^{1,1}$ coefficients	1998	Hart F. Smith
+ PDF Chat	On the critical semilinear wave equation outside convex obstacles	1995	Hart F. Smith Christopher D. Sogge
+	Generalized Strichartz Inequalities for the Wave Equation	1995	J. Ginibre G. Velo
+	On Existence and Scattering with Minimal Regularity for Semilinear Wave Equations	1995	Hans Lindblad Christopher D. Sogge
+	A variational formulation of schrödinger-poisson systems in dimension d ≤ 3	1993	Francis Nier
+	Parametrix and propagation of singularities for the interior mixed hyperbolic problem	1977	Gregory Eskin