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Descripción
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| In a previus paper (see [1] in references) we introduced a class of 1−d wave equations with rapidly oscillating H¿older continuous coefficients for which the classical boundary observability property fails. We also established that these examples could be used to contradict Strichartz-type inequalities for the wave equation with low regularity coefficients. The object of this Note is to further analyze this issue. As we will see, the argument in [1] only provides sharp counterexamples to the Strichartz estimates when the coefficient belongs to L1. We carefully analyze this counterexamples for H¿older continuous coefficients. We also give a new application of our construction showing that some eigenfunction estimates for elliptic operators due to Sogge can fail when coefficients are not smooth enough. | |
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Internacional
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Si |
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JCR del ISI
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Si |
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Título de la revista
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ARCH RATION MECH AN |
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ISSN
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0003-9527 |
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Factor de impacto JCR
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1,96 |
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Información de impacto
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Volumen
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185 |
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DOI
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Número de revista
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3 |
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Desde la página
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365 |
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Hasta la página
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377 |
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Mes
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SIN MES |
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Ranking
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