A note on the a.e. second-order differentiability of rank-one convex functions
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911260952494080 |
|---|---|
| author | Hirsch, Jonas |
| author_facet | Hirsch, Jonas |
| contents | In the Euclidean setting, the well-known Alexandrov theorem states that convex functions are twice differentiable almost everywhere. In this note, we extend this theorem to rank-one convex functions. Our approach is novel in that it draws more from viscosity techniques developed in the context of fully nonlinear elliptic equations. As a byproduct, the original Alexandrov theorem can essentially be reduced to the a.e. differentiability of one-dimensional monotone functions, as presented in the appendix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the a.e. second-order differentiability of rank-one convex functions Hirsch, Jonas Analysis of PDEs 26B05, 49J45 (Primary) 26B25, 35B65 (Secondary) In the Euclidean setting, the well-known Alexandrov theorem states that convex functions are twice differentiable almost everywhere. In this note, we extend this theorem to rank-one convex functions. Our approach is novel in that it draws more from viscosity techniques developed in the context of fully nonlinear elliptic equations. As a byproduct, the original Alexandrov theorem can essentially be reduced to the a.e. differentiability of one-dimensional monotone functions, as presented in the appendix. |
| title | A note on the a.e. second-order differentiability of rank-one convex functions |
| topic | Analysis of PDEs 26B05, 49J45 (Primary) 26B25, 35B65 (Secondary) |
| url | https://arxiv.org/abs/2511.08397 |