Lerner, M. E.; Repin, O. A. A boundary value problem for mixed-type equations in domains with multiply connected hyperbolicity subdomains. (Russian, English) Zbl 1049.35146 Sib. Mat. Zh. 44, No. 1, 160-177 (2003); translation in Sib. Math. J. 44, No. 1, 132-146 (2003). The authors study a boundary value problem for the Lavrent’ev–Bitsadze equations \[ u_{xx}+\text{sgn } y\cdot u_{yy}=0 \] and for the general Lavrent’ev–Bitsadze equation \[ u_{xx}+\text{sgn }y\cdot u_{yy}+A(x,y)u_{x}+B(x,y)u_{y}+C(x,y)u=0 \] in domains with unbounded multiply connected hyperbolicity subdomains. Moreover, the ellipticity and hyperbolicity domains are assumed infinite. For this problem the authors prove an analog of the maximum principle as well as uniqueness and existence theorems. In the case of the Lavrent’ev–Bitsadze equation the solution is presented in an explicit form. Reviewer: A. I. Kozhanov (Novosibirsk) MSC: 35M10 PDEs of mixed type Keywords:Lavrent’ev-Bitsadze equation; infinite domain; maximum principle; existence and uniqueness PDFBibTeX XMLCite \textit{M. E. Lerner} and \textit{O. A. Repin}, Sib. Mat. Zh. 44, No. 1, 160--177 (2003; Zbl 1049.35146); translation in Sib. Math. J. 44, No. 1, 132--146 (2003) Full Text: EuDML EMIS