Multidimensional Zaremba problem for the $$p(\,\cdot\,)$$-Laplace equation. A Boyarsky–Meyers estimate
Yu. A. Alkhutov, Gregory Aleksandrovich Chechkin · Theoretical and Mathematical Physics · 2024
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.