Boundary regularity and sufficient conditions for strong local minimizers

Cordero, Judith Campos

doi:10.1016/j.jfa.2017.02.027

Cited by 15 publications

(14 citation statements)

References 43 publications

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“…The regularity of strong W 1,p -minimisers was first considered by Kristensen & Taheri [44], who established a partial regularity theorem in the case of superquadratic (p ≥ 2) growth. These results have been extended for instance in [13,60,10,11].…”

Section: Extension To Strong Local Minimisersmentioning

confidence: 83%

Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth

Irving¹

2021

Preprint

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A partial regularity theorem is presented for minimisers of k thorder functionals subject to a quasiconvexity and general growth condition. We will assume a natural growth condition governed by an N -function satisfying the ∆ 2 and ∇ 2 conditions, assuming no quantitative estimates on the second derivative of the integrand; this is new even in the k = 1 case. These results will also be extended to the case of strong local minimisers.

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Section: Extension To Strong Local Minimisersmentioning

confidence: 83%

Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth

Irving¹

2021

Preprint

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“…Next, we present a series of lemmas that are crucial for the proof of Theorem 5.1. Lemma 5.3 below provides some crucial properties of G, and its proof, originating in [1], is based on [9]. PROOF.…”

Section: An Averaged Convexity-type Bound For Quasiconvex Functionsmentioning

confidence: 98%

“…Lemma 5.3 below provides some crucial properties of G, and its proof, originating in [1], is based on [9]. Lemma 5.3 below provides some crucial properties of G, and its proof, originating in [1], is based on [9].…”

Section: An Averaged Convexity-type Bound For Quasiconvex Functionsmentioning

confidence: 99%

“…Its proof, motivated by the works in [1,9,10,30], is based on the calculus of variations and it is postponed until Section 5, where a precise statement is also given. These include our functional setting as well as a brief summary on Young measures and quasiconvexity.…”

Section: Introductionmentioning

confidence: 99%

“…We stress that Theorem 5.1 is independent of the equations, and it is of broader interest. Its proof, motivated by the works in [1,9,10,30], is based on the calculus of variations and it is postponed until Section 5, where a precise statement is also given.…”

Section: Introductionmentioning

confidence: 99%

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Quasiconvex Elastodynamics: Weak‐Strong Uniqueness for Measure‐Valued Solutions

Koumatos

Spirito

2018

Comm Pure Appl Math

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A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the material is assumed to be strongly quasiconvex. The proof employs tools from the calculus of variations to establish general convexity-type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics.

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