Variational competition between full Hessian and its determinant for convex functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866914664455077888 |
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| author | Gladbach, Peter Olbermann, Heiner |
| author_facet | Gladbach, Peter Olbermann, Heiner |
| contents | We prove upper and lower bounds for a variational functional for convex functions satisfying certain boundary conditions on a sector of the unit ball in two dimensions. The functional contains two terms: The full Hessian and its determinant, where the former is treated as a small perturbation in the space $L^2$ and the latter as the leading-order term, in the negative Sobolev space $W^{-2,2}$. We point out how this setting is motivated by problems in nonlinear elasticity, and obtain a corollary for a variational problem based on the so-called Föppl-von-Kármán energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_06109 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Variational competition between full Hessian and its determinant for convex functions Gladbach, Peter Olbermann, Heiner Analysis of PDEs 49Q10, 74K20 We prove upper and lower bounds for a variational functional for convex functions satisfying certain boundary conditions on a sector of the unit ball in two dimensions. The functional contains two terms: The full Hessian and its determinant, where the former is treated as a small perturbation in the space $L^2$ and the latter as the leading-order term, in the negative Sobolev space $W^{-2,2}$. We point out how this setting is motivated by problems in nonlinear elasticity, and obtain a corollary for a variational problem based on the so-called Föppl-von-Kármán energy. |
| title | Variational competition between full Hessian and its determinant for convex functions |
| topic | Analysis of PDEs 49Q10, 74K20 |
| url | https://arxiv.org/abs/1907.06109 |