Geodesic
$L_2$-estimates for solutions of the general boundary-value problems for the equations with mixed parabolic-elliptic structure
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 4-27

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$L_2$-estimates for solutions of the model boundary value problems — Cauchy problem and semispace problem — for linear equation $L\left(\frac\partial{\partial x}, \frac\partial{\partial t}\right)u=0$ in which operator $L$ is product $2b_1$-parabolic operator and $2b_2r$-elliptic operator ($b_1$, $b_2$, $r$ — integer numbers) are obtained. 
@article{ZNSL_1992_197_a0,
     author = {M. A. Abdrachmanov},
     title = {$L_2$-estimates for solutions of the general boundary-value problems for the equations with mixed parabolic-elliptic structure},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {4--27},
     publisher = {mathdoc},
     volume = {197},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a0/}
}
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M. A. Abdrachmanov. $L_2$-estimates for solutions of the general boundary-value problems for the equations with mixed parabolic-elliptic structure. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 23, Tome 197 (1992), pp. 4-27. http://geodesic.mathdoc.fr/item/ZNSL_1992_197_a0/