Asymptotic Analysis· 2026Q1
Asymptotically Quasiconvex Functionals with General Growth Conditions
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- 2026year
Short summary
Minimizers of vectorial integrals with general growth conditions are C1,α regular at points where the gradient is large and excess is small, and Lipschitz on a dense open subset.
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Key points
- Partial regularity results are proven for minimizers of autonomous vectorial integrals.
- C1,α regularity is achieved at points with large gradient and small excess.
- Lipschitz regularity is obtained on a dense open subset of the domain.
- Results apply to pairs of Young functions satisfying specific structural assumptions.
AI-generated from the title and abstract; the full text is not read.
Abstract
We establish partial regularity results for minimizers of autonomous vectorial integrals in the Calculus of Variations, under ψ -growth conditions and assuming φ -quasiconvexity only in an asymptotic sense, both in subquadratic and superquadratic regimes. More precisely, we prove that minimizers are of class C 1 , α at points x 0 where D u is sufficiently large in a neighborhood of x 0 and where the excess is sufficiently small, and we obtain Lipschitz regularity on a dense open subset of the domain. These results apply to pairs of Young functions ( φ , ψ ) satisfying the structural assumptions ( H .0 ) – ( H .4 ) , which are strictly stronger than the classical Δ 2 condition.
The authors' abstract, as published at the source. Asymptotic Analysis, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics