Multidimensional Zaremba problem for the $$p(\,\cdot\,)$$-Laplace equation. A Boyarsky–Meyers estimate

2024

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DOI 10.1134/s004057792401001x
Data confidence 70 medium
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Abstract

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.