Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces

Vagif S. Guliyev, and Mehriban N. Omarova. "Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces." Open Mathematics 14.1 (2016): 49-61. <http://eudml.org/doc/276911>.

@article{VagifS2016,
abstract = {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)$\dot\{W\}_\{2,1\}^\{p,\varphi \}\left( \{Q,\omega \} \right)$.},
author = {Vagif S. Guliyev, Mehriban N. Omarova},
journal = {Open Mathematics},
keywords = {Generalized weighted Morrey spaces; Uniformly parabolic operators; Regular oblique derivative problem; VMO; generalized weighted Morrey spaces; uniformly parabolic operators; regular oblique derivative problem},
language = {eng},
number = {1},
pages = {49-61},
title = {Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces},
url = {http://eudml.org/doc/276911},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Vagif S. Guliyev
AU - Mehriban N. Omarova
TI - Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 49
EP - 61
AB - 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)$\dot{W}_{2,1}^{p,\varphi }\left( {Q,\omega } \right)$.
LA - eng
KW - Generalized weighted Morrey spaces; Uniformly parabolic operators; Regular oblique derivative problem; VMO; generalized weighted Morrey spaces; uniformly parabolic operators; regular oblique derivative problem
UR - http://eudml.org/doc/276911
ER -