Lower semicontinuity for polyconvex integrals without coercivity assumptions

Micol Amar; Virginia De Cicco

doi:10.3934/eect.2014.3.363

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2014, Volume 3, Issue 3: 363-372. Doi: 10.3934/eect.2014.3.363

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Lower semicontinuity for polyconvex integrals without coercivity assumptions

Micol Amar^1, and
Virginia De Cicco^1,

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza - Università di Roma, Via A. Scarpa 16, 00161 Roma

Received: April 30, 2013

Revised: October 31, 2013

Published: August 2014

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Abstract

We prove a lower semicontinuity theorem for a polyconvex functional of integral form, related to maps $u:\Omega \subset \mathbb{R}^{n}\rightarrow \mathbb{R}^{m}$ in $W^{1,n}(\Omega ;\mathbb{R}^{m})$ with $n\geq m\geq 2$, with respect to the weak $W^{1,p}$-convergence for $p>m-1$, without assuming any coercivity condition.

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Mathematics Subject Classification: Primary: 49J45; Secondary: 49K20.

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References

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