REMOVABLE SETS FOR THE WAVE EQUATIONS IN TERMS OF HAUSDORFF MEASURE

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Résumé

We prove a Radó theorem for the wave equations. Namely, we
consider u to be a locally Lipschitz continuous function on an
open set X of R^{n+1} and weakly solution to the wave equations ∂ttu -div(∇u)=0
away from the zero set away from the zero set u^{-1}(0) in X. We prove
that u is a weak solution to these wave equations in all of X .

Mots-clés

hyperbolic equations, removable sets, Hausdorff measure.