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On some analog of the Bitsadze–Samarskij problem. (English. Russian original) Zbl 0916.35043

Sib. Math. J. 40, No. 1, 153-157 (1999); translation from Sib. Mat. Zh. 40, No. 1, 177-182 (1999).
Consider the degenerate elliptic equation \[ y^mu_{xx}+u_{yy}+a(x,y)u_y+b(x,y)u_x+c(x,y)u=0 \tag{1} \] in a subdomain \(\Omega\) of the upper half-plane. The author studies a boundary value problem for (1) with some special nonlocal Bitsadze-Samarskij conditions given on a part of the boundary of \(\Omega\) and some mixed condition with fractional derivatives given on the degeneration line (the latter may coincide with the Dirichlet or Holmgren condition in particular cases).
For the problem under study, the authors prove an analog of the maximum principle as well as uniqueness and existence theorems.

MSC:

35J70 Degenerate elliptic equations
35B50 Maximum principles in context of PDEs
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