Geodesic
Quasi-elliptic equations with degeneration
Matematičeskie zametki SVFU, Tome 28 (2021), pp. 48-57.

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We study the solvability of boundary value problems for some classes of degenerate quasi-elliptic equations. The main feature of the problems under study is that, despite the degeneration, boundary conditions should still be imposed on the boundary manifolds. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives required in the equation in the inner subdomains. Moreover, we describe some possible enhancements and generalizations of the obtained results.
Mots-clés : quasi-elliptic equations, existence
Keywords: degeneration, boundary value problem, regular solution, uniqueness. 
@article{SVFU_2021_28_a3,
     author = {A. I. Kozhanov and G. A. Varlamova},
     title = {Quasi-elliptic equations with degeneration},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {48--57},
     publisher = {mathdoc},
     volume = {28},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2021_28_a3/}
}
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A. I. Kozhanov; G. A. Varlamova. Quasi-elliptic equations with degeneration. Matematičeskie zametki SVFU, Tome 28 (2021), pp. 48-57. http://geodesic.mathdoc.fr/item/SVFU_2021_28_a3/