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Microlocal properties of the problem with a singular oblique derivative in a neighbourhood of diffractive points. (English. Russian original) Zbl 0607.35065
Russ. Math. Surv. 41, No. 1, 223-224 (1986); translation from Usp. Mat. Nauk 41, No. 1, 179-180 (1980).
The paper gives a necessary and sufficient condition for the boundary problem \[ (D^ 2_ y-D_{x_ 0}| D_{x'}| -yD^ 2_{x'})u=f\quad on\quad \{(y,x_ 0,x_ 1,...,x_ n),y>0,\quad x_ i\in R,i=0,1,...,n\}, \]
\[ (x^ k_ n D_ y+cD_ x)u| =_{y=0}g,u|_{x<T}\in C^{\infty};\quad D^ 2_{x'}=\sum^{n}_{i=1}D^ 2_{x_ i}) \] to be hypoelliptic (by the definition given in the paper) in a diffractive point.
Reviewer: M.Kopáčková
MSC:
35L80 Degenerate hyperbolic equations
65H10 Numerical computation of solutions to systems of equations
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
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