Geodesic
On Dirichlet-type problems for the Lavrent'ev--Bitsadze equation
Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 242-249

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The existence and uniqueness issues are discussed for several boundary value problems with Dirichlet data for the Lavrent'ev–Bitsadze equation in a mixed domain. A general mixed problem (according to Bitsadze's terminology) is considered in which the Dirichlet data are relaxed on a hyperbolic region of the boundary inside a characteristic sector with vertex on the type-change interval. In particular, conditions are pointed out under which the problem is uniquely solvable for any choice of this vertex. 
@article{TRSPY_2012_278_a21,
     author = {A. P. Soldatov},
     title = {On {Dirichlet-type} problems for the {Lavrent'ev--Bitsadze} equation},
     journal = {Informatics and Automation},
     pages = {242--249},
     publisher = {mathdoc},
     volume = {278},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a21/}
}
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A. P. Soldatov. On Dirichlet-type problems for the Lavrent'ev--Bitsadze equation. Informatics and Automation, Differential equations and dynamical systems, Tome 278 (2012), pp. 242-249. http://geodesic.mathdoc.fr/item/TRSPY_2012_278_a21/