Geodesic
A polyharmonic equation on the sphere in the three-dimensional space
Matematičeskie zametki SVFU, Tome 29 (2022) no. 3, pp. 22-31 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a nonhomogeneous polyharmonic equation on the unit sphere in the three-dimensional Euclidean space. Sobolev spherical spaces act as functional classes in which solutions to the spherical polyharmonic equation are sought. It is proved that for a given right-hand side of the equation, which is orthogonal to the identically-one function, the solution to the equation exists in the spherical Sobolev space and is unique there. We establish that for small variations of the right-hand side of the polyharmonic equation under consideration, its solutions change little in the corresponding norm.
Mots-clés : polyharmonic equation
Keywords: spherical Sobolev spaces, extremal functions. 
@article{SVFU_2022_29_3_a1,
     author = {V. L. Vaskevich},
     title = {A polyharmonic equation on the sphere in the three-dimensional space},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {22--31},
     year = {2022},
     volume = {29},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_3_a1/}
}
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V. L. Vaskevich. A polyharmonic equation on the sphere in the three-dimensional space. Matematičeskie zametki SVFU, Tome 29 (2022) no. 3, pp. 22-31. http://geodesic.mathdoc.fr/item/SVFU_2022_29_3_a1/