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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2409.08713 |
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Table des matières:
- We show higher integrability of minimisers of functionals \[ I(u) = \int_Ω f(x,u(x)) ~\mathrm{d}x \] subject to a differential constraint $\mathscr{A} u=0$ under natural $p$-growth and $p$-coercivity conditions for $f$ and regularity assumptions on $Ω$. For the differential operator $\mathscr{A}$ we asssume a rather abstract truncation property that, for instance, holds for operators $\mathscr{A}=\mathrm{curl}$ and $\mathscr{A}=\mathrm{div}$. The proofs are based on the comparison of the minimiser to the truncated version of the minimiser.