Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces
We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w)...
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De Gruyter
2016-01-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2016-0006 |
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doaj-3afb8bae768e4bbba592e2abf0bcaea42021-09-06T19:20:07ZengDe GruyterOpen Mathematics2391-54552016-01-01141496110.1515/math-2016-0006math-2016-0006Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spacesGuliyev Vagif S.0Omarova Mehriban N.1Ahi Evran University, Department of Mathematics, 40100, Kirsehir, Turkey and Institute of Mathematics and Mechanics, AZ 1141 Baku, AzerbaijanInstitute of Mathematics and Mechanics, AZ 1141 Baku, Azerbaijan and Baku State University, Baku, AZ 1148, AzerbaijanWe obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space W˙2,1p,φ(Q,ω)$\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.https://doi.org/10.1515/math-2016-0006generalized weighted morrey spacesuniformly parabolic operatorsregular oblique derivative problemvmo35k2035d3535b4535r05 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Guliyev Vagif S. Omarova Mehriban N. |
| spellingShingle |
Guliyev Vagif S. Omarova Mehriban N. Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces Open Mathematics generalized weighted morrey spaces uniformly parabolic operators regular oblique derivative problem vmo 35k20 35d35 35b45 35r05 |
| author_facet |
Guliyev Vagif S. Omarova Mehriban N. |
| author_sort |
Guliyev Vagif S. |
| title |
Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces |
| title_short |
Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces |
| title_full |
Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces |
| title_fullStr |
Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces |
| title_full_unstemmed |
Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces |
| title_sort |
parabolic oblique derivative problem with discontinuous coefficients in generalized weighted morrey spaces |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2016-01-01 |
| description |
We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space W˙2,1p,φ(Q,ω)$\dot W_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$. |
| topic |
generalized weighted morrey spaces uniformly parabolic operators regular oblique derivative problem vmo 35k20 35d35 35b45 35r05 |
| url |
https://doi.org/10.1515/math-2016-0006 |
| work_keys_str_mv |
AT guliyevvagifs parabolicobliquederivativeproblemwithdiscontinuouscoefficientsingeneralizedweightedmorreyspaces AT omarovamehribann parabolicobliquederivativeproblemwithdiscontinuouscoefficientsingeneralizedweightedmorreyspaces |
| _version_ |
1717777268220100608 |