On a generalized Wirtinger inequality

Croce, Gisella; Dacorogna, Bernard

doi:10.3934/dcds.2003.9.1329

Cited by 30 publications

(21 citation statements)

References 7 publications

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“…In contrast to this, the minimizers are not antisymmetric when N = 2 and p is sufficiently large. A similar break of symmetry was already observed in [13], [12], [17], [3], [11], [20] for the minimizers of the functional…”

Section: Introductionsupporting

confidence: 79%

Symmetry and asymmetry of minimizers of a class of noncoercive functionals

Brock

Croce

Guibé

et al. 2017

Advances in Calculus of Variations

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Abstract. In this paper we prove symmetry results for minimizers of a non coercive functional defined on the class of Sobolev functions with zero mean value. We prove that the minimizers are foliated Schwarz symmetric, i.e. they are axially symmetric with respect to an axis passing through the origin and nonincreasing in the polar angle from this axis. In the two dimensional case we show a symmetry breaking.

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Section: Introductionsupporting

confidence: 79%

Symmetry and asymmetry of minimizers of a class of noncoercive functionals

Brock

Croce

Guibé

et al. 2017

Advances in Calculus of Variations

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“…The case of equality holds if and only if A = {(x, y) ∈ R 2 : |x| p ′ + |y| p ′ = 1}, up to a translation and a dilation. Several other results are available in the one-dimensional case, see for instance [5], [4], [2], [19], [11] and the references therein for further details.…”

Section: Introductionmentioning

confidence: 99%

An isoperimetric inequality for a nonlinear eigenvalue problem

Croce

Henrot

Pisante

2012

Ann. Inst. H. Poincaré C Anal. Non Linéaire

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“…This inequality ensures that the modeling error decreases by the minimization of the model derivative error and its magnitude is guaranteed to be lower than the scaled magnitude of model derivative error with respect to the 2-norm. Notice that Wirtinger’s inequality has been generalized to any L p norm 53 thus showing that the level of accuracy of the model derivative implies a corresponding level of accuracy for the model according to any L p norm.…”

Section: Propositionmentioning

confidence: 99%

In vivo and in vitro comparative assessment of the log-linearized Hunt–Crossley model for impact-contact modeling in physical human–robot interactions

Courrèges

Laribi

Arsicault

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part I:

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In physical human–robot interactions, making the robot perceive in real time the mechanical contact impedance is critical for interactions safety, robot control and haptic rendering for robot teleoperation and can be achieved through online parametric model identification. Probing the viscoelastic properties of tissues is also a medical concern. For soft viscoelastic biological tissues, the Hunt–Crossley model is a contact force model computationally inexpensive while being accurate. As this model is non-linear, a log linear approximation has been proposed to achieve a fast and real-time identification using a recursive least squares approach. In this article, we want to regard the log-linearized expression of the Hunt–Crossley model no more as an approximation, but rather as a valuable empirical mechanical model of soft biological tissues. We show through experimental data fit and sophisticated statistical analysis that the log-linearized Hunt–Crossley model performs always closely to the Hunt–Crossley model and is even often slightly better. The experimental conditions investigated are related to impact and contact interactions, relevant in the context of Cobotics.

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On a generalized Wirtinger inequality

Abstract: We show thatgeneralizing results of Dacorogna-Gangbo-Subía and others.

Cited by 30 publications

References 7 publications

Symmetry and asymmetry of minimizers of a class of noncoercive functionals

Symmetry and asymmetry of minimizers of a class of noncoercive functionals

An isoperimetric inequality for a nonlinear eigenvalue problem

In vivo and in vitro comparative assessment of the log-linearized Hunt–Crossley model for impact-contact modeling in physical human–robot interactions

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