Article Dans Une Revue Journal of Differential Equations Année : 2004

Oscillating minimizers of a fourth order problem invariant under scaling

Résumé

By variational methods, we prove the inequality \Ru2dx\Ruu2dxI\Ru4dxuL4(\R)such thatuL2(\R)
for some constant I(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.

Dates et versions

hal-00157514 , version 1 (26-06-2007)

Identifiants

Citer

Isabelle Catto, Jean Dolbeault, Rafael Benguria, Régis Monneau. Oscillating minimizers of a fourth order problem invariant under scaling. Journal of Differential Equations, 2004, 205 (1), pp.253-269. ⟨10.1016/j.jde.2004.03.024⟩. ⟨hal-00157514⟩
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