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- W2565190248 abstract "Abstract We state necessary and sufficient conditions for weak lower semicontinuity of integral functionals of the form ${umapstoint_{Omega}h(x,u(x)),mathrm{d}x}$ , where h is continuous and possesses a positively p -homogeneous recession function, ${p>1}$ , and ${uin L^{p}(Omega;mathbb{R}^{m})}$ lives in the kernel of a constant-rank first-order differential operator ${mathcal{A}}$ which admits an extension property. In the special case ${mathcal{A}=mathrm{curl}}$ , apart from the quasiconvexity of the integrand, the recession function’s quasiconvexity at the boundary in the sense of Ball and Marsden is known to play a crucial role. Our newly defined notions of ${mathcal{A}}$ -quasiconvexity at the boundary, generalize this result. Moreover, we give an equivalent condition for the weak lower semicontinuity of the above functional along sequences weakly converging in ${L^{p}(Omega;mathbb{R}^{m})}$ and approaching the kernel of ${mathcal{A}}$ even if ${mathcal{A}}$ does not have the extension property." @default.
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- W2565190248 date "2017-01-01" @default.
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- W2565190248 title "𝒜$mathcal{A}$-quasiconvexity at the boundary and weak lower semicontinuity of integral functionals" @default.
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- W2565190248 doi "https://doi.org/10.1515/acv-2015-0009" @default.
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