Oblique derivative problems for second-order hyperbolic equations with degenerate curve

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.

Keywords

• Oblique derivative problem
• hyperbolic equations
• degenerate curve