We provide relaxation for not lower semicontinuous supremal functionals defined on vectorial Lipschitz functions, where the Borel level convex density depends only on the gradient. The connection with indicator functionals is also enlightened, thus extending previous lower semicontinuity results in that framework. Finally, we discuss the power law approximation of supremal functionals, with nonnegative, coercive densities having explicit dependence also on the spatial variable, and satisfying minimal measurability assumptions.
A relaxation result in the vectorial setting and power law approximation for supremal functionals / Prinari &, Francesca; Zappale, Elvira. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 1573-2878. - 186:2(2020), pp. 412-452. [https://doi.org/10.1007/s10957-020-01712-y]
A relaxation result in the vectorial setting and power law approximation for supremal functionals.
Elvira Zappale
2020
Abstract
We provide relaxation for not lower semicontinuous supremal functionals defined on vectorial Lipschitz functions, where the Borel level convex density depends only on the gradient. The connection with indicator functionals is also enlightened, thus extending previous lower semicontinuity results in that framework. Finally, we discuss the power law approximation of supremal functionals, with nonnegative, coercive densities having explicit dependence also on the spatial variable, and satisfying minimal measurability assumptions.File | Dimensione | Formato | |
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