On the Boyarsky--Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift
Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 1-14
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We establish the increased integrability of the gradient of the solution to the Dirichlet problem for the Laplace operator with lower terms and prove the unique solvability of this problem.
Keywords:
Zaremba problem, Meyers estimates, embedding theorems, increased integrability.
@article{CMFD_2024_70_1_a0,
author = {Yu. A. Alkhutov and G. A. Chechkin},
title = {On the {Boyarsky--Meyers} estimate for the solution of the {Dirichlet} problem for a second-order linear elliptic equation with drift},
journal = {Contemporary Mathematics. Fundamental Directions},
pages = {1--14},
publisher = {mathdoc},
volume = {70},
number = {1},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CMFD_2024_70_1_a0/}
}
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%0 Journal Article %A Yu. A. Alkhutov %A G. A. Chechkin %T On the Boyarsky--Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift %J Contemporary Mathematics. Fundamental Directions %D 2024 %P 1-14 %V 70 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMFD_2024_70_1_a0/ %G ru %F CMFD_2024_70_1_a0
Yu. A. Alkhutov; G. A. Chechkin. On the Boyarsky--Meyers estimate for the solution of the Dirichlet problem for a second-order linear elliptic equation with drift. Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 1, pp. 1-14. http://geodesic.mathdoc.fr/item/CMFD_2024_70_1_a0/