We prove the lower semicontinuity of functionals of the form ∫ΩV(α)d|Eu|, with respect to the weak converge of alpha in W-1,W-gamma (Omega), gamma > 1, and the weak* convergence of u in BD (Omega), where Omega subset of R-n. These functional arise in the variational modelling of linearised elasto-plasticity coupled with damage and their lower semicontinuity is crucial in the proof of existence of quasi-static evolutions. This is the first result achieved for subcritical exponents gamma < n.
A lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,γ, γ > 1 / Crismale, Vito; Orlando, Gianluca. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - ELETTRONICO. - 2:1(2020), pp. 101-118. [10.3934/mine.2020006]
A lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,γ, γ > 1
Orlando, Gianluca
2020-01-01
Abstract
We prove the lower semicontinuity of functionals of the form ∫ΩV(α)d|Eu|, with respect to the weak converge of alpha in W-1,W-gamma (Omega), gamma > 1, and the weak* convergence of u in BD (Omega), where Omega subset of R-n. These functional arise in the variational modelling of linearised elasto-plasticity coupled with damage and their lower semicontinuity is crucial in the proof of existence of quasi-static evolutions. This is the first result achieved for subcritical exponents gamma < n.| File | Dimensione | Formato | |
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