Oblique derivative problem for quasilinear mixed equations with parabolic degeneracy in multiply connected domains

Abstract

This article deals with the oblique derivative problem for second order quasilinear equations of mixed type in multiply connected domains, which includes the Tricomi problem of the Chaplygin equation in gas dynamics as a special case. We first give the representation of solutions of the boundary value problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, using complex functions in the domain of ellipticity and hyperbolic complex functions in the domain where the equation is hyperbolic.

Keywords:

• oblique derivative problem
• quasilinear mixed equations
• parabolic degeneracy
• multiply connected domains

AMS Subject Classifications:

• 35K65
• 35M05
• 35L80