Electron. J. Diff. Eqns.,
Vol. 2009(2009), No. 65, pp. 116.
Oblique derivative problems for generalized Rassias equations
of mixed type with several characteristic boundaries
Guo Chun Wen
Abstract:
This article concerns the oblique derivative problems for
secondorder 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 LeraySchauder 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 secondorder 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
,
,
which was posed as
an open problem by Rassias.
Submitted December 16, 2008. Published May 14, 2009.
Math Subject Classifications: 35M05, 35J70, 35L80.
Key Words: Oblique derivative problems; generalized Rassias equations;
several characteristic boundaries.
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Guo Chun Wen
LMAM, School of Mathematical Sciences
Peking University, Beijing 100871, China
email: Wengc@math.pku.edu.cn

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