Geodesic
Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky–Meyers estimate
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 3-22 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the higher integrability of the gradient of solutions of the Zaremba problem in a bounded strongly Lipschitz domain for an inhomogeneous $p(\,\cdot\,)$-Laplace equation with a variable exponent $p$ having a logarithmic continuity modulus.
Keywords: Zaremba problem, Meyers estimates, capacity, embedding theorems, higher integrability. 
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Yu. A. Alkhutov; G. A. Chechkin. Multidimensional Zaremba problem for the $p(\,\cdot\,)$-laplace equation. A Boyarsky–Meyers estimate. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 1, pp. 3-22. http://geodesic.mathdoc.fr/item/TMF_2024_218_1_a0/

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