Geodesic
Asymptotic analysis of an elliptic boundary-value problem in a wedge
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 3-9

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In this paper, we consider an elliptic pseudodifferential equation, whose symbol is independent of the spatial variable, in a wedge-shaped domain of a multidimensional space. Under a special wave factorization of the symbol, we construct in the Sobolev–Slobodetskii space the general solution of the equation, which depends on one arbitrary function. The equation is supplemented by an integral condition, which allows one to extract a unique solution. We examine the behavior of this solution in the case where the aperture of the wedge tends to zero.
Keywords: pseudodifferential operator, elliptic boundary-value problem, wave factorization of a symbol, general solution, asymptotic behavior, solvability condition. 
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     title = {Asymptotic analysis of an elliptic boundary-value problem in a wedge},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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V. B. Vasilev (Vasilyev); Sh. Kutaiba; A. Z. Yaduta. Asymptotic analysis of an elliptic boundary-value problem in a wedge. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 3-9. http://geodesic.mathdoc.fr/item/INTO_2021_195_a0/