Data di Pubblicazione:
2015
Citazione:
Higher order functional inequalities related to the clamped 1-biharmonic operator / E. Parini, B. Ruf, C. Tarsi. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 194:6(2015 Dec), pp. 1835-1858. [10.1007/s10231-014-0447-x]
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
higher order Sobolev embeddding; minimization problem; clamped 1-biharmonic operator; Faber-Krahn type inequality
Elenco autori:
E. Parini, B. Ruf, C. Tarsi
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