On complex-valued solutions to a 2D Eikonal equation. Part three: analysis of a Bäcklund transformation
作者： Rolando Magnanini , Giorgio Talenti
DOI: 10.1080/00036810500277041
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摘要: The following equation and related partial differential equations systems, which arise in a generalization of geometrical optics, are investigated from theoretical point view. Here x y denote rectangular coordinates the Euclidean plane, n is real-valued, strictly positive smooth enough. Qualitative properties solutions were derived Magnanini Talenti (1999, On complex-valued to 2D Eikonal equation. Part One: qualitative properties. Contemporary Mathematics, 283, 203–229). Partial governing Re(w) treated (2002, Complex-Valued Solutions Equation. Two: Existence Theorems. SIAM Journal on Mathematical Analysis, 34, 805–835). we put use viscosity variational methods, Backlund transformation relating Im (w).
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