Geodesic
Oblique derivative problems for generalized Rassias equations of mixed type with several characteristic boundaries
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This article concerns the oblique derivative problems for second-order quasilinear degenerate equations of mixed type with several characteristic boundaries, which include the Tricomi problem as a special case. First we formulate the problem and obtain estimates of its solutions, then we show the existence of solutions by the successive iterations and the Leray-Schauder theorem. We use a complex analytic method: elliptic complex functions are used in the elliptic domain, and hyperbolic complex functions in the hyperbolic domain, such that second-order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients. An application of the complex analytic method, solves (1.1) below with $m=n=1, a=b=0$, which was posed as an open problem by Rassias.
Classification : 35M05, 35J70, 35L80
Keywords: oblique derivative problems, generalized rassias equations, several characteristic boundaries 
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     author = {Wen, Guo Chun},
     title = {Oblique derivative problems for generalized {Rassias} equations of mixed type with several characteristic boundaries},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2009},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a137/}
}
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Wen, Guo Chun. Oblique derivative problems for generalized Rassias equations of mixed type with several characteristic boundaries. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a137/