# Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 5, page 1357-1388
- ISSN: 1435-9855

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topIvanovici, Oana. "Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary." Journal of the European Mathematical Society 014.5 (2012): 1357-1388. <http://eudml.org/doc/277363>.

@article{Ivanovici2012,

abstract = {In this paper we consider a smooth and bounded domain $\Omega \subset \mathbb \{R\}^d$ of dimension $d\ge 2$ 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 $\mathbb \{R\}^d$.},

author = {Ivanovici, Oana},

journal = {Journal of the European Mathematical Society},

keywords = {microlocal analysis; wave equation; Dirichlet boundary condition; Strichartz estimates; propagation and reflection of singularities; conormal waves with cusps; caustics; gliding point; Dirichlet boundary conditions; propagation and reflection of singularities; conormal waves with cusps; caustics; gliding point},

language = {eng},

number = {5},

pages = {1357-1388},

publisher = {European Mathematical Society Publishing House},

title = {Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary},

url = {http://eudml.org/doc/277363},

volume = {014},

year = {2012},

}

TY - JOUR

AU - Ivanovici, Oana

TI - Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary

JO - Journal of the European Mathematical Society

PY - 2012

PB - European Mathematical Society Publishing House

VL - 014

IS - 5

SP - 1357

EP - 1388

AB - In this paper we consider a smooth and bounded domain $\Omega \subset \mathbb {R}^d$ of dimension $d\ge 2$ 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 $\mathbb {R}^d$.

LA - eng

KW - microlocal analysis; wave equation; Dirichlet boundary condition; Strichartz estimates; propagation and reflection of singularities; conormal waves with cusps; caustics; gliding point; Dirichlet boundary conditions; propagation and reflection of singularities; conormal waves with cusps; caustics; gliding point

UR - http://eudml.org/doc/277363

ER -

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