Oblique Derivative Problems for Second Order Equations of Mixed Type in Multiply Connected Domains

Abstract

In this paper, oblique derivative boundary value problems for second order equations of mixed (elliptic-hyperbolic) type in multiply connected domains is discussed. Firstly the representation of solutions forthe above boundary value problem is given, afterwards the uniqueness and existence of solutions of the above problem are stated. In book [1], the author proposed the Dirichlet boundary value problem (Tricomi problem) forsecond order equations of mixed type in multiply connected domains. In [2, 3], the author only discussed the Dirichlet problem (Tricomi T 2) for the equation u xx +sgny u yy = 0 in a special doubly connected domain. Up to now we have not seen that other authors have solved it in multiply connected domains. In the present paper, we try to discuss the oblique derivative problem for second order equations of mixed type in multiply connected domains, which includes the Dirichlet problem (Problem T 2) as a special case.Key wordsoblique derivative problemsequations of mixed typemultiply connected domains.