Geodesic
Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary
Journal of the European Mathematical Society, Tome 14 (2012) no. 5, pp. 1357-1388 Cet article a éte moissonné depuis la source EMS Press

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In this paper we consider a smooth and bounded domain Ω⊂Rd of dimension d≥2 with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of the usual range of indices. This is due to microlocal phenomena such as caustics generated in arbitrarily small time near the boundary. Moreover, the result holds for microlocally strictly convex domains in Rd.
DOI : 10.4171/jems/335
Classification : 35-XX, 58-XX, 00-XX
Keywords: Microlocal analysis, wave equation, Dirichlet boundary condition, Strichartz estimates, propagation and reflection of singularities, conormal waves with cusps, caustics 
@article{JEMS_2012_14_5_a1,
     author = {Oana Ivanovici},
     title = {Counterexamples to the {Strichartz} inequalities for the wave equation in general domains with boundary},
     journal = {Journal of the European Mathematical Society},
     pages = {1357--1388},
     year = {2012},
     volume = {14},
     number = {5},
     doi = {10.4171/jems/335},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/335/}
}
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Oana Ivanovici. Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary. Journal of the European Mathematical Society, Tome 14 (2012) no. 5, pp. 1357-1388. doi: 10.4171/jems/335

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