Variants of Bernstein's theorem for variational integrals with linear and nearly linear growth
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929246528602112 |
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| author | Bildhauer, Michael Fuchs, Martin |
| author_facet | Bildhauer, Michael Fuchs, Martin |
| contents | Using a Caccioppoli-type inequality involving negative exponents for a directional weight we establish variants of Bernstein's theorem for variational integrals with linear and nearly linear growth. We give some mild conditions for entire solutions of the equation \[ {\rm div} \Big[Df(\nabla u)\Big] = 0 \, , \] under which solutions have to be affine functions. Here $f$ is a smooth energy density satisfying $D^2 f>0$ together with a natural growth condition for $D^2 f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variants of Bernstein's theorem for variational integrals with linear and nearly linear growth Bildhauer, Michael Fuchs, Martin Analysis of PDEs 49Q20, 49Q05, 53A10, 35J20 Using a Caccioppoli-type inequality involving negative exponents for a directional weight we establish variants of Bernstein's theorem for variational integrals with linear and nearly linear growth. We give some mild conditions for entire solutions of the equation \[ {\rm div} \Big[Df(\nabla u)\Big] = 0 \, , \] under which solutions have to be affine functions. Here $f$ is a smooth energy density satisfying $D^2 f>0$ together with a natural growth condition for $D^2 f$. |
| title | Variants of Bernstein's theorem for variational integrals with linear and nearly linear growth |
| topic | Analysis of PDEs 49Q20, 49Q05, 53A10, 35J20 |
| url | https://arxiv.org/abs/2402.11225 |