On the Boyarsky–Meyers estimate for the gradient of the solution to the Dirichlet problem for the second order elliptic equation with drift. The case the critical Sobolev exponen

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Abstract

The increased integrability of the gradient of the solution to the Increased integrability of the gradient o the solution to the homogeneous Dirichlet problem for the Poisson equation with lower terms in a bounded Lipschitz domain is established. A proof of the unique solvability of this problem is also given.

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About the authors

Yu. A. Alkhutov

Vladimir State University named after Alexander and Nikolay Stoletovs

Author for correspondence.
Email: yurij-alkhutov@yandex.ru
Russian Federation, Vladimir

A. G. Chechkina

Lomonosov Moscow State University; Ufa Science Center of the Russian Academy of Sciences

Email: chechkina@gmail.com

Institute of Mathematics with Computer Center

Russian Federation, Moscow; Ufa

References

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  5. Giaquinta M., Modica G. Regularity results for some classes of higher order nonlinear elliptic systems // Journ. für die reine und angewandte Math. 1979. V. 311/312. P. 145–169.
  6. Skrypnik I.V. Methods for Analysis of Nonlinear Elliptic Boundary Value Problems, Translations of Math.Monographs, AMS, Providence. 1994. V. 139. 1994.
  7. Chechkin G.A. The Meyers Estimates for Domains Perforated along the Boundary // Mathematics. 2021. V. 9. N 23. Art number 3015.
  8. Чечкин Г.А., Чечкина Т.П. Оценка Боярского–Мейерса для дивергентных эллиптических уравнений второго порядка. Два пространственных примера // Проблемы математического анализа. 2022. Т. 119. С. 107–116.

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