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- W2012193685 abstract "A detailed study of solutions to the rst order partial dier- ential equation H(x;y;zx;zy) = 0, with special emphasis on the eikonal equation z 2 + z 2 y = h(x;y), is made near points where the equation be- comes 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 elds." @default.
- W2012193685 created "2016-06-24" @default.
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- W2012193685 date "2000-03-21" @default.
- W2012193685 modified "2023-10-18" @default.
- W2012193685 title "Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables" @default.
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- W2012193685 doi "https://doi.org/10.21236/ada640692" @default.
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