Oscillating minimizers of a fourth order problem invariant under scaling

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dc.creatorBenguria, R.
dc.creatorCatto, I.
dc.creatorDolbeault, J.
dc.creatorMonneau, R.
dc.date2003-11-12
dc.date.accessioned2026-07-07T05:02:49Z
dc.date.available2026-07-07T05:02:49Z
dc.descriptionBy variational methods, we prove the inequality: $$ \int_{\mathbb{R}} u''{}^2 dx-\int_{\mathbb{R}} u'' u^2 dx\geq I \int_{\mathbb{R}} u^4 dx\quad \forall u\in L^4({\mathbb{R}}) {such that} u''\in L^2({\mathbb{R}}) $$ for some constant $I\in (-9/64,-1/4)$. This inequality is connected to Lieb-Thirring type problems and has interesting scaling properties. The best constant is achieved by sign changing minimizers of a problem on periodic functions, but does not depend on the period. Moreover, we completely characterize the minimizers of the periodic problem.
dc.description19 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0311192
dc.identifierhttp://arxiv.org/abs/math/0311192
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69164
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35J35; 26D20; 47J20; 49J40
dc.titleOscillating minimizers of a fourth order problem invariant under scaling
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