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$\mathcal{A}$-quasiconvexity, Gårding inequalities, and applications in PDE constrained problems in dynamics and statics
journal contribution
posted on 2023-06-10, 00:20 authored by Konstantinos KoumatosKonstantinos Koumatos, Andreas Panagiotis VikelisA Gårding-type inequality is proved for a quadratic form associated to $\mathcal{A}$-quasiconvex functions. This quadratic form appears as the relative entropy in the theory of conservation laws and it is related to the Weierstrass excess function in the calculus of variations. The former provides weak-strong uniqueness results, whereas the latter has been used to provide sufficiency theorems for local minimizers. Using this new Gårding inequality we provide an extension of these results to PDE constrained problems in dynamics and statics under $\mathcal{A}$-quasiconvexity assumptions. The application in statics improves existing results by proving uniqueness of $L^p$-local minimizers in the classical $\mathcal{A}={curl}$ case.
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- Published
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- Accepted version
Journal
SIAM Journal on Mathematical AnalysisISSN
0036-1410Publisher
Society for Industrial and Applied MathematicsExternal DOI
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4Volume
53Page range
4178-4211Department affiliated with
- Mathematics Publications
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- Yes
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- Yes
Legacy Posted Date
2021-07-15First Open Access (FOA) Date
2021-07-15First Compliant Deposit (FCD) Date
2021-07-15Usage metrics
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