Given a family of locally Lipschitz vector fields X(x) = (X1(x),..., Xm(x)) on R n, m < n, we study integral functionals depending on X. Using the results in [A. Maione, A. Pinamonti, and F. Serra Cassano, J. Math. Pures Appl. (9), 139 (2020), pp. 109-142], we study the convergence of minima, minimizers, and momenta of those functionals. Moreover, we apply these results to the periodic homogenization in Carnot groups and prove an H-compactness theorem for linear differential operators of the second order depending on X.
Γ-Convergence for Functionals Depending on Vector Fields. II. Convergence of Minimizers
Maione, Alberto;
2022-01-01
Abstract
Given a family of locally Lipschitz vector fields X(x) = (X1(x),..., Xm(x)) on R n, m < n, we study integral functionals depending on X. Using the results in [A. Maione, A. Pinamonti, and F. Serra Cassano, J. Math. Pures Appl. (9), 139 (2020), pp. 109-142], we study the convergence of minima, minimizers, and momenta of those functionals. Moreover, we apply these results to the periodic homogenization in Carnot groups and prove an H-compactness theorem for linear differential operators of the second order depending on X.File in questo prodotto:
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