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Article Dans Une Revue Annali di Matematica Pura ed Applicata Année : 2014

Higher-order functional inequalities related to the clamped 1-biharmonic operator

Enea Parini
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Bernhard Ruf
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Cristina Tarsi
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Résumé

We consider the problem of finding the optimal constant for the embedding of the space W2,1Δ,0(Ω):={u∈W1,10(Ω)∣∣there exists {uk}⊂C∞c(Ω) s.t. ∥Δuk−Δu∥1→0} into the space L1(Ω), where Ω⊂ℝn is a bounded domain with boundary of class C1,1. This is equivalent to find the first eigenvalue Λc1,1(Ω) of the clamped 1-biharmonic operator. In this paper, we identify the correct relaxation of the problem on BL0(Ω), the space of functions whose distributional Laplacian is a finite Radon measure, we obtain the associated Euler–Lagrange equation, and we give lower bounds for Λc1,1(Ω), investigating the validity of an inequality of Faber–Krahn type.

Dates et versions

hal-01266562 , version 1 (02-02-2016)

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Citer

Enea Parini, Bernhard Ruf, Cristina Tarsi. Higher-order functional inequalities related to the clamped 1-biharmonic operator. Annali di Matematica Pura ed Applicata, 2014, 194 (6), pp.1835-1858. ⟨10.1007/s10231-014-0447-x⟩. ⟨hal-01266562⟩
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