A geometric reduction method for some fully nonlinear first-order PDEs on semi-Riemannian manifolds
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911940328030208 |
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| author | Fernández, Juan Carlos Guerra-Velasco, Eddaly Palmas, Oscar Percino-Figueroa, Boris A. |
| author_facet | Fernández, Juan Carlos Guerra-Velasco, Eddaly Palmas, Oscar Percino-Figueroa, Boris A. |
| contents | Given a semi-Riemannian manifold $(M,\langle \cdot,\cdot\rangle_g),$ we use the transnormal functions defined on $M$ to reduce fully nonlinear first order PDEs of the form \[ F(x,u,\langle \nabla_g u, \nabla_g u \rangle_g) = 0,\qquad \text{on }M \] into ODEs and obtain local existence results of solutions which are constant along the level sets of the transnormal functions. In particular, we apply this reduction method to obtain new solutions to eikonal equations with a prescribed geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01954 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A geometric reduction method for some fully nonlinear first-order PDEs on semi-Riemannian manifolds Fernández, Juan Carlos Guerra-Velasco, Eddaly Palmas, Oscar Percino-Figueroa, Boris A. Analysis of PDEs 34A05, 35B06, 35F20, 53C21, 58J70 Given a semi-Riemannian manifold $(M,\langle \cdot,\cdot\rangle_g),$ we use the transnormal functions defined on $M$ to reduce fully nonlinear first order PDEs of the form \[ F(x,u,\langle \nabla_g u, \nabla_g u \rangle_g) = 0,\qquad \text{on }M \] into ODEs and obtain local existence results of solutions which are constant along the level sets of the transnormal functions. In particular, we apply this reduction method to obtain new solutions to eikonal equations with a prescribed geometry. |
| title | A geometric reduction method for some fully nonlinear first-order PDEs on semi-Riemannian manifolds |
| topic | Analysis of PDEs 34A05, 35B06, 35F20, 53C21, 58J70 |
| url | https://arxiv.org/abs/2407.01954 |