Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.02121 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- We study differential inclusions $Du\in Π$ in an open set $Ω\subset\mathbb R^2$, where $Π\subset \mathbb R^{2\times 2}$ is a compact connected $C^2$ curve without rank-one connections, but non-elliptic: tangent lines to $Π$ may have rank-one connections, so that classical regularity and rigidity results do not apply. For a wide class of such curves $Π$, we show that $Du$ is locally Lipschitz outside a discrete set, and is rigidly characterized around each singularity. Moreover, in the partially elliptic case where at least one tangent line to $Π$ has no rank-one connections, or under some topological restrictions on the tangent bundle of $Π$, there are no singularities. This goes well beyond previously known particular cases related to Burgers' equation and to the Aviles-Giga functional. The key is the identification and appropriate use of a general underlying structure: an infinite family of conservation laws, called entropy productions in reference to the theory of scalar conservation laws.