We introduce a notion of quasiconvexity for continuous functions f defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold (M, g) and ℝ^m, naturally generalizing the classical Euclidean definition. We prove that this condition characterizes the sequential lower semicontinuity of the associated integral functional (formula presented) with respect to the weak* topology of W^1,∞(Ω, R^m), for every bounded open subset Ω⊂ M.
Quasiconvexity in the Riemannian setting / Corbisiero, A., Leone, C., Mantegazza, C.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1720-0768. - 36:4(2025), pp. 763-779. [10.4171/RLM/1089]
Quasiconvexity in the Riemannian setting
Corbisiero A.;Leone C.;Mantegazza C.
2025
Abstract
We introduce a notion of quasiconvexity for continuous functions f defined on the vector bundle of linear maps between the tangent spaces of a smooth Riemannian manifold (M, g) and ℝ^m, naturally generalizing the classical Euclidean definition. We prove that this condition characterizes the sequential lower semicontinuity of the associated integral functional (formula presented) with respect to the weak* topology of W^1,∞(Ω, R^m), for every bounded open subset Ω⊂ M.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
