Lower semicontinuity for functionals with (p, q)-growth in Carnot groups |
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Authors: | Costantino Capozzoli |
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Institution: | 1. Dipartimento di Matematica e Applicazioni ??R. Caccioppoli??, Universit?? di Napoli ??Federico II??, Via Cintia, 80126, Naples, Italy
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Abstract: | Let ?? be a bounded open subset of ${\mathbb{G}}$ , where ${\mathbb{G}}$ is a Carnot group, and let ${u: \Omega \rightarrow \mathbb{R}^d}$ be a vector valued function. We prove a lower semicontinuity result in the weak topology of the horizontal Sobolev space ${W^{1,p}_X(\Omega,\mathbb{R}^d)}$ , with p?>?1, of the integral functional of the calculus of variations of the type $$F(u)=\int\limits_\Omega f(Xu)\,dx$$ where f is a X-quasiconvex function satisfying a non-standard growth conditions and Xu is the horizontal gradient of u. |
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