Oscillating minimizers of a fourth-order problem invariant under scaling

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• 作者：Benguria ; Rafael D. ; Catto ; Isabelle ; Dolbeault ; Jean ; Monneau ; Ré ; gis
• 关键词：Minimization ; Inequalities ; Fourth-order operators ; Loss of compactness ; Scaling invariance ; Euler&ndash ; Lagrange equation ; Lagrange multiplier ; Lieb&ndash ; Thirring inequalities ; Commutator method for Lieb&ndash ; Thirring inequalities ; Shooting method
• 刊名：Journal of Differential Equations
• 出版年：2004
• 出版时间：October 1, 2004
• 年：2004
• 卷：205
• 期：1
• 页码：253-269
• 全文大小：271 K

文摘

By variational methods, we prove the inequality Formula Not Shown for some constant I(−,−). 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.