RUS  ENG
Full version
JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2022 Volume 519, Pages 229–263 (Mi znsl7308)

Estimates of solutions to the noncoercive Dirichlet problem for a second order elliptic equation in divergence form with drift from a Kato class

M. D. Surnachev

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

Abstract: For a second order linear elliptic equation with uniformly elliptic principal part in divergence form and drift from a Kato–Stummel type class we establish the unique solvability and estimates of solutions of the corresponding noncoercive Dirichlet problem.

Key words and phrases: noncoercive Dirichlet problem, Kato–Stummel classes, unique solvability, stationary convection-diffusion equation, drift.

UDC: 517

Received: 01.12.2022



© Steklov Math. Inst. of RAS, 2024