$\mathscr{A}$-free truncation and higher integrability of minimisers
| Autor: | Schiffer, Stefan |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show higher integrability of minimisers of functionals \[ I(u) = \int_{\Omega} f(x,u(x)) ~\mathrm{d}x \] subject to a differential constraint $\mathscr{A} u=0$ under natural $p$-growth and $p$-coercivity conditions for $f$ and regularity assumptions on $\Omega$. 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. Comment: 16 pages |
| Databáze: | arXiv |
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