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Mathematical analysis demonstrates gradient estimates for weakly monotone quasilinear equations, enabling large-scale homogenization of p-Laplace systems.
In this manuscript, we provide local Lq-estimates for the gradient of solutions of a class of quasilinear equations whose principal part lacks strong monotonicity. These estimates are used to establish uniform large-scale Lq-estimates for the gradient of solutions of degenerate/singular quasilinear equations with oscillating coefficients and large-scale Lipschitz estimates for solutions of non-degenerate equations.
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Koch et al. (2026) studied this question.
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