Geodesic
Elliptic problems in domains with degenerate singularities
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 50-56

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We consider a model elliptic pseudodifferential equation in Sobolev– Slobodetsky spaces in a reflex angle on the plane. Using the wave factorization, in the case of a unique solution, we study the situation where the aperture of the explementary angle tends to zero. We prove that this limit exists only if the right-hand side satisfies a certain additional condition and obtain this condition using the properties of singular integral operators.
Keywords: pseudodifferential equation, wave factorization, planar angle, singular integral, boundary condition.
Mots-clés : symbol, limit solution 
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     author = {V. B. Vasilev (Vasilyev) and Sh. Kutaiba},
     title = {Elliptic problems in domains with degenerate singularities},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {50--56},
     publisher = {mathdoc},
     volume = {216},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_216_a4/}
}
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V. B. Vasilev (Vasilyev); Sh. Kutaiba. Elliptic problems in domains with degenerate singularities. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 216 (2022), pp. 50-56. http://geodesic.mathdoc.fr/item/INTO_2022_216_a4/