Geodesic
Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 497 (2021), pp. 3-6

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An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.
Keywords: Meyers estimates, embedding theorems, rapidly changing type of boundary conditions. 
@article{DANMA_2021_497_a0,
     author = {Yu. A. Alkhutov and G. A. Chechkin},
     title = {Increased integrability of the gradient of the solution to the {Zaremba} problem for the {Poisson} equation},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {3--6},
     publisher = {mathdoc},
     volume = {497},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_497_a0/}
}
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Yu. A. Alkhutov; G. A. Chechkin. Increased integrability of the gradient of the solution to the Zaremba problem for the Poisson equation. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 497 (2021), pp. 3-6. http://geodesic.mathdoc.fr/item/DANMA_2021_497_a0/