Comptes Rendus
Short paper
The Meyer’s estimate of solutions to Zaremba problem for second-order elliptic equations in divergent form
Yurij A. Alkhutov1; Gregory A. Chechkin2, 3, 4  
1 A.G. and N.G. Stoletov Vladimir State University, Gor’kogo St., 87, Vladimir, 600000, Russia
2 Institute of Mathematics and Mathematical Modeling, Pushkin st. 125, Almaty, 050010, Kazakhstan
3 Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Chernyshevskogo st., 112, Ufa, 450008, Russia
4 M.V. Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russia
Comptes Rendus. Mécanique, Volume 349 (2021) no. 2, pp. 299-304.

In this paper we obtain an estimate for the increased integrability of the gradient of the solution to the Zaremba problem for divergent elliptic operator in a bounded domain with nontrivial capacity of the Dirichlet boundary conditions.

Dans cet article, nous obtenons une estimation de l’intégrabilité accrue du gradient de la solution du problème de Zaremba pour un opérateur elliptique divergent dans un domaine borné avec une capacité non triviale des conditions aux limites de Dirichlet.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmeca.87
Keywords: Meyers estimates, Mixed problem, Embedding theorems, Capacity, Rapidly alternating type of boundary conditions
Mot clés : Estimations de Meyers, Problème mixte, Théorèmes d’intégration, Capacité, Type de conditions aux limites à alternance rapide
Yurij A. Alkhutov 1; Gregory A. Chechkin 2, 3, 4

1 A.G. and N.G. Stoletov Vladimir State University, Gor’kogo St., 87, Vladimir, 600000, Russia
2 Institute of Mathematics and Mathematical Modeling, Pushkin st. 125, Almaty, 050010, Kazakhstan
3 Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Chernyshevskogo st., 112, Ufa, 450008, Russia
4 M.V. Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, 119991, Russia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Yurij A. Alkhutov; Gregory A. Chechkin. The Meyer’s estimate of solutions to Zaremba problem for second-order elliptic equations in divergent form. Comptes Rendus. Mécanique, Volume 349 (2021) no. 2, pp. 299-304. doi : 10.5802/crmeca.87. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.87/

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