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arXiv · 2306.17768

Asymptotically quasiconvex functionals with general growth conditions

Francesca Angrisani
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Abstract

We establish local regularity results for minimizers of autonomous vectorial integrals of Calculus of Variations, assuming $\psi$-growth conditions and imposing $\varphi$-quasiconvexity only in an asymptotic sense, both in the sub-quadratic and super-quadratic case. In particular, we obtain $C^{1,\alpha}$ regularity at points $x_0$ where $Du$ is sufficiently large in a neighborhood of $x_0$, as well as Lipschitz regularity on a dense set. \ The results hold for all pairs of Young functions $(\varphi, \psi)$ satisfying the $\Delta_2$ condition.

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Francesca Angrisani. 2023-06-30. Asymptotically quasiconvex functionals with general growth conditions. https://arxiv.org/abs/2306.17768

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