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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.15982 |
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| _version_ | 1866915450593476608 |
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| author | Katzourakis, Nikos Moser, Roger |
| author_facet | Katzourakis, Nikos Moser, Roger |
| contents | For an elliptic, semilinear differential operator of the form $S(u) = A : D^2 u + b(x, u , Du)$, consider the functional $E_\infty(u) = \mathop{\mathrm{ess \, sup}}_Ω|S(u)|$. We study minimisers of $E_\infty$ for prescribed boundary data. Because the functional is not differentiable, this problem does not give rise to a conventional Euler-Lagrange equation. Under certain conditions, we can nevertheless give a system of partial differential equations that all minimisers must satisfy. Moreover, the condition is equivalent to a weaker version of the variational problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15982 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Variational problems in $L^\infty$ involving semilinear second order differential operators Katzourakis, Nikos Moser, Roger Analysis of PDEs For an elliptic, semilinear differential operator of the form $S(u) = A : D^2 u + b(x, u , Du)$, consider the functional $E_\infty(u) = \mathop{\mathrm{ess \, sup}}_Ω|S(u)|$. We study minimisers of $E_\infty$ for prescribed boundary data. Because the functional is not differentiable, this problem does not give rise to a conventional Euler-Lagrange equation. Under certain conditions, we can nevertheless give a system of partial differential equations that all minimisers must satisfy. Moreover, the condition is equivalent to a weaker version of the variational problem. |
| title | Variational problems in $L^\infty$ involving semilinear second order differential operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2303.15982 |