Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 36, pp. 1-14.
Title: Oblique derivative problems for second-order hyperbolic equations
with degenerate curve
Author: Guo-Chun Wen (Peking Univ., Beijing, China)
Abstract:
The present article concerns the oblique derivative problem
for second order hyperbolic equations with degenerate circle arc.
Firstly the formulation of the oblique derivative problem for
the equations is given, next the representation and estimates
of solutions for the above problem are obtained, moreover the
existence of solutions for the problem is proved by the successive
iteration of solutions of the equations. In this article, we
use the complex analytic method, namely the new partial
derivative notations, hyperbolic complex functions are
introduced, such that the second order hyperbolic equations with
degenerate curve are reduced to the first order hyperbolic complex
equations with singular coefficients, then the advantage of complex
analytic method can be applied.
Submitted December 22, 2010. Published March 03, 2011.
Math Subject Classifications: 35L20, 35L80.
Key Words: Oblique derivative problem; hyperbolic equations;
degenerate curve.