Yu. A. Alkhutov, A. G. Chechkina, “On the Boyarsky–Meyers estimate for the gradient of the solution to the Dirichlet problem for a second-order linear elliptic equation with drift: The case of critical Sobolev exponent”, Dokl. RAN. Math. Inf. Proc. Upr., 2024, Volume 516,Pages <nobr>87

MATHEMATICS

On the Boyarsky–Meyers estimate for the gradient of the solution to the Dirichlet problem for a second-order linear elliptic equation with drift: The case of critical Sobolev exponent

Yu. A. Alkhutov^a, A. G. Chechkina^bc

^a Vladimir State University, Vladimir, Russia
^b Lomonosov Moscow State University, Moscow, Russia
^c Ufa Federal Research Centre of the Russian Academy of Sciences

Abstract: Increased integrability of the gradient of the solution to the homogeneous Dirichlet problem for the Poisson equation with lower terms in a bounded Lipschitz domain is established. The unique solvability of this problem is also proved.

Keywords: elliptic equation, lower coefficients, Dirichlet problem, Meyers estimate, existence and uniqueness of solution.

UDC: 517.954 + 517.982

Presented: V. V. Kozlov
Received: 20.02.2024
Revised: 25.03.2024
Accepted: 25.03.2024

DOI: 10.31857/S2686954324020149