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Mapping properties of one class of quasielliptic operators. / Demidenko, Gennadii.
Mathematics and Computing - 3rd International Conference, ICMC 2017, Proceedings. Springer-Verlag GmbH and Co. KG, 2017. стр. 339-348 (Communications in Computer and Information Science; Том 655).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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TY - GEN
T1 - Mapping properties of one class of quasielliptic operators
AU - Demidenko, Gennadii
N1 - Publisher Copyright: © Springer Nature Singapore Pte Ltd. 2017.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - The paper is devoted to the theory of quasielliptic operators. We consider scalar and homogeneous quasielliptic operators L(Dx) with lower terms in the whole space ℝn . Our aim is to study mapping properties of these operators in weighted Sobolev spaces. We introduce a special scale of weighted Sobolev spaces Wl p,q,σ(ℝn). These spaces coincide with known spaces of Sobolev type for some parameters l, q, σ. We investigate mapping properties of the operators L(Dx) in the spaces Wp,q,σ(ℝn). We indicate conditions for unique solvability of quasielliptic equations and systems in these spaces, obtain estimates for solutions and formulate an isomorphism theorem for quasielliptic operators. To prove our results we construct special regularizers for quasielliptic operators.
AB - The paper is devoted to the theory of quasielliptic operators. We consider scalar and homogeneous quasielliptic operators L(Dx) with lower terms in the whole space ℝn . Our aim is to study mapping properties of these operators in weighted Sobolev spaces. We introduce a special scale of weighted Sobolev spaces Wl p,q,σ(ℝn). These spaces coincide with known spaces of Sobolev type for some parameters l, q, σ. We investigate mapping properties of the operators L(Dx) in the spaces Wp,q,σ(ℝn). We indicate conditions for unique solvability of quasielliptic equations and systems in these spaces, obtain estimates for solutions and formulate an isomorphism theorem for quasielliptic operators. To prove our results we construct special regularizers for quasielliptic operators.
KW - Isomorphism
KW - Quasielliptic operators
KW - Weighted Sobolev spaces
UR - http://www.scopus.com/inward/record.url?scp=85018385738&partnerID=8YFLogxK
U2 - 10.1007/978-981-10-4642-1_29
DO - 10.1007/978-981-10-4642-1_29
M3 - Conference contribution
AN - SCOPUS:85018385738
SN - 9789811046414
T3 - Communications in Computer and Information Science
SP - 339
EP - 348
BT - Mathematics and Computing - 3rd International Conference, ICMC 2017, Proceedings
PB - Springer-Verlag GmbH and Co. KG
T2 - 3rd International Conference on Mathematics and Computing, ICMC 2017
Y2 - 17 January 2017 through 21 January 2017
ER -
ID: 10262746