Higher-order functional inequalities related to the clamped 1-biharmonic operator
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| 001 | 605496161 | ||
| 003 | CHVBK | ||
| 005 | 20210128100535.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-014-0447-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0447-x | ||
| 245 | 0 | 0 | |a Higher-order functional inequalities related to the clamped 1-biharmonic operator |h [Elektronische Daten] |c [Enea Parini, Bernhard Ruf, Cristina Tarsi] |
| 520 | 3 | |a We consider the problem of finding the optimal constant for the embedding of the space $$\begin{aligned} W^{2,1}_{\Delta ,0}(\Omega ) := \{ u \in W^{1,1}_0(\Omega )\,\big |\,\text {there exists } \{u_k\} \subset C_c^\infty (\Omega ) \text { s.t. }\Vert \Delta u_k - \Delta u\Vert _1 \rightarrow 0 \} \end{aligned}$$ W Δ , 0 2 , 1 ( Ω ) : = { u ∈ W 0 1 , 1 ( Ω ) | there exists { u k } ⊂ C c ∞ ( Ω ) s.t. ‖ Δ u k - Δ u ‖ 1 → 0 } into the space $$L^1(\Omega )$$ L 1 ( Ω ) , where $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n is a bounded domain with boundary of class $$C^{1,1}$$ C 1 , 1 . This is equivalent to find the first eigenvalue $$\Lambda _{1,1}^c(\Omega )$$ Λ 1 , 1 c ( Ω ) of the clamped 1-biharmonic operator. In this paper, we identify the correct relaxation of the problem on $$BL_0(\Omega )$$ B L 0 ( 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 $$\Lambda _{1,1}^c(\Omega )$$ Λ 1 , 1 c ( Ω ) , investigating the validity of an inequality of Faber-Krahn type. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Higher order Sobolev embeddding |2 nationallicence | |
| 690 | 7 | |a Minimization problem |2 nationallicence | |
| 690 | 7 | |a Clamped 1-biharmonic operator |2 nationallicence | |
| 690 | 7 | |a Faber-Krahn type inequality |2 nationallicence | |
| 700 | 1 | |a Parini |D Enea |u CNRS, Centrale Marseille, I2M, UMR 7373, Aix Marseille Université, 13453, Marseille, France |4 aut | |
| 700 | 1 | |a Ruf |D Bernhard |u Dipartimento di Matematica "Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy |4 aut | |
| 700 | 1 | |a Tarsi |D Cristina |u Dipartimento di Matematica "Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1835-1858 |x 0373-3114 |q 194:6<1835 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0447-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0447-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Parini |D Enea |u CNRS, Centrale Marseille, I2M, UMR 7373, Aix Marseille Université, 13453, Marseille, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ruf |D Bernhard |u Dipartimento di Matematica "Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Tarsi |D Cristina |u Dipartimento di Matematica "Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/6(2015-12-01), 1835-1858 |x 0373-3114 |q 194:6<1835 |1 2015 |2 194 |o 10231 | ||