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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Resumo

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.

Sobre autores

Yu. Alkhutov

Vladimir State University named after Alexander and Nikolay Stoletovs

Autor responsável pela correspondência
Email: yurij-alkhutov@yandex.ru
Rússia, Vladimir

A. Chechkina

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

Email: chechkina@gmail.com

Institute of Mathematics with Computer Center

Rússia, Moscow; Ufa

Bibliografia

  1. Боярский Б.В. Обобщенные решения системы дифференциальных уравнений первого порядка эллиптического типа с разрывными коэффициентами // Матем. сб. 1957. Т. 43. № 85. С. 451–503
  2. Meyers N.G. An Lp –estimate for the gradient of solutions of second order elliptic deivergence equations // Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 3-e série. 1963. V. 17. N 3. P. 189–206.
  3. Гилбарг Д., Трудингер Н.С. Эллиптические дифференциальные уравнения с частными производными второго порядка. М.: Наука, 1989.
  4. Gehring F.W. The Lp —integrability of the partial derivatives of a quasiconformal mapping // Acta Math. 1973. V. 130. P. 265–277.
  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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