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Uniqueness of a solution of the problem $$T$$ for an equation of mixed type with conjugation of the normal derivative with the fractional derivative. (English. Russian original) Zbl 1084.35533
Russ. Math. 47, No. 9, 4-7 (2003); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2003, No. 9, 6-9 (2003).
From the text: The following equation is considered: $U_{xx}+ \text{sgn}\,y\cdot U_{yy}-\lambda U=0,\;\lambda>0$ in the domain $$G$$ bounded by the smooth curve $$\Gamma$$, which lies in the half-plane $$y>0$$ and has the ends $$A(0;0)$$ and $$B(1;0)$$ (the origin of the curve is at the point $$B)$$, and segments of the characteristics $$AC:y=-x$$, $$BC:y=x-1$$, $$C(1/2;-1/2)$$.

##### MSC:
 35M10 PDEs of mixed type 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
characteristics