Extension of convex functions from a hyperplane to a half-space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909154494382080 |
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| author | Ball, John M. Horner, Christopher L. |
| author_facet | Ball, John M. Horner, Christopher L. |
| contents | It is shown that a possibly infinite-valued proper lower semicontinuous convex function on ${\mathbb R}^n$ has an extension to a convex function on the half-space ${\mathbb R}^n\times[0,\infty)$ which is finite and smooth on the open half-space ${\mathbb R}^n\times(0,\infty)$. The result is applied to nonlinear elasticity, where it clarifies how the condition of polyconvexity of the free-energy density $ψ(Dy)$ is best expressed when $ψ(A)\to\infty$ as $\det A\to 0+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02671 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extension of convex functions from a hyperplane to a half-space Ball, John M. Horner, Christopher L. Analysis of PDEs 26B25 49J45 74B20 It is shown that a possibly infinite-valued proper lower semicontinuous convex function on ${\mathbb R}^n$ has an extension to a convex function on the half-space ${\mathbb R}^n\times[0,\infty)$ which is finite and smooth on the open half-space ${\mathbb R}^n\times(0,\infty)$. The result is applied to nonlinear elasticity, where it clarifies how the condition of polyconvexity of the free-energy density $ψ(Dy)$ is best expressed when $ψ(A)\to\infty$ as $\det A\to 0+$. |
| title | Extension of convex functions from a hyperplane to a half-space |
| topic | Analysis of PDEs 26B25 49J45 74B20 |
| url | https://arxiv.org/abs/2311.02671 |