Geodesic
Mixed biharmonic Dirichlet--Neumann problem in exterior domains
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 755-762

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We study the unique solvability of the mixed Dirichlet–Neumann problem for the biharmonic equation in the exterior of a compact set under the assumption that solutions of this problem have bounded Dirichlet integrals with the weight $|x|^a$. Depending on the value of the parameter $a$, we obtained uniqueness (non-uniqueness) theorems of the problem and present exact formulas for the dimension of the space of solutions of the mixed Dirichlet–Neumann problem.
Keywords: biharmonic operator, Dirichlet–Neumann problem, weighted Dirichlet integral. 
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     author = {Hovik A. Matevossian},
     title = {Mixed biharmonic {Dirichlet--Neumann} problem in exterior domains},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {755--762},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a8/}
}
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Hovik A. Matevossian. Mixed biharmonic Dirichlet--Neumann problem in exterior domains. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 755-762. http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a8/