TY - JOUR
ID - 244074
TI - Interior Schauder-Type Estimates for Higher-Order Elliptic Operators in Grand-Sobolev Spaces
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Bilalov, Bilal
AU - Sadigova, Sabina Rahib
AD - Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
AD - Khazar University, Baku, Azerbaijan and Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.
Y1 - 2021
PY - 2021
VL - 18
IS - 2
SP - 129
EP - 148
KW - Elliptic operator
KW - Higher-order
KW - Interior Schauder-type Estimates
KW - Grand-Sobolev space
DO - 10.22130/scma.2021.521544.893
N2 - In this paper an elliptic operator of the $m$-th order $L$ with continuous coefficients in the $n$-dimensional domain $Omega subset R^{n} $ in the non-standard Grand-Sobolev space $W_{q)}^{m} left(Omega right), $ generated by the norm $left| , cdot , right| _{q)} $ of the Grand-Lebesgue space $L_{q)} left(Omega right), $ is considered. Interior Schauder-type estimates play a very important role in solving the Dirichlet problem for the equation $Lu=f$. The considered non-standard spaces are not separable, and therefore, to use classical methods for treating solvability problems in these spaces, one needs to modify these methods. To this aim, based on the shift operator, separable subspaces of these spaces are determined, in which finite infinitely differentiable functions are dense. Interior Schauder-type estimates are established with respect to these subspaces. It should be noted that Lebesgue spaces $L_{q} left(Gright), $ are strict parts of these subspaces. This work is a continuation of the authors of the work cite{28}, which established the solvability in the small of higher order elliptic equations in grand-Sobolev spaces.
UR - https://scma.maragheh.ac.ir/article_244074.html
L1 - https://scma.maragheh.ac.ir/article_244074_10d98a26bec3cb9947f17137508ea500.pdf
ER -