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

@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 -