Asymptotically quasiconvex functionals with general growth conditions

2023/06/30 by Francesca Angrisani, Angrisani, Francesca
Computer Science · Mathematics · #35B65 #35J47 #46E30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2306.17768

openalex publication_date 2023/06/30 · openalex created_date 2023/07/04 · openalex updated_date 2026/08/04

Abstract

We establish local regularity results for minimizers of autonomous vectorial integrals of Calculus of Variations, assuming ψ-growth conditions and imposing φ-quasiconvexity only in an asymptotic sense, both in the sub-quadratic and super-quadratic case. In particular, we obtain C^1,α regularity at points x₀ where Du is sufficiently large in a neighborhood of x₀, as well as Lipschitz regularity on a dense set. The results hold for all pairs of Young functions (φ, ψ) satisfying the Δ₂ condition.

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