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arXiv · 2212.12821

$\mathcal{A}$-harmonic approximation and partial regularity, revisited

Matthias Bärlin·Franz Gmeineder·Christopher Irving·Jan Kristensen
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Abstract

We give a direct harmonic approximation lemma for local minima of quasiconvex multiple integrals that entails their $\mathrm{C}^{1,\alpha}$ or $\mathrm{C}^{\infty}$-partial regularity. Different from previous contributions, the method is fully direct and elementary, only hinging on the $\mathrm{L}^{p}$-theory for strongly elliptic linear systems and Sobolev's embedding theorem. Especially, no heavier tools such as Lipschitz truncations are required.

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Matthias Bärlin, Franz Gmeineder, Christopher Irving, Jan Kristensen. 2022-12-24. $\mathcal{A}$-harmonic approximation and partial regularity, revisited. https://arxiv.org/abs/2212.12821

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