Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
| dc.creator | Cornea, Emil | |
| dc.creator | Howard, Ralph | |
| dc.creator | Martinsson, Per-Gunnar | |
| dc.date | 2000-01-28 | |
| dc.date.accessioned | 2026-07-07T04:33:29Z | |
| dc.date.available | 2026-07-07T04:33:29Z | |
| dc.description | A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equation becomes singular in the sense that dH=0, in which case the method of characteristics does not apply. The main results are that there is a strong lack of uniqueness of solutions near such points and that solutions can be less regular than both the function H and the initial data of the problem, but that this loss of regularity only occurs along a pair of curves through the singular point. The main tools are symplectic geometry and the Sternberg normal form for Hamiltonian vector fields. | |
| dc.description | 29 pages. See also http://www.math.sc.edu/~howard/ | |
| dc.identifier | https://arxiv.org/abs/math/0001172 | |
| dc.identifier | http://arxiv.org/abs/math/0001172 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58593 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 35F20 | |
| dc.title | Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables | |
| dc.type | text |