Mathematical analysis provides an estimate for integrability of gradients in Zaremba problem solutions, suggesting implications for Dirichlet and Neumann conditions.
An estimate for the increased integrability is obtained for the gradient of the solution to the Zaremba problem for Poisson's equation with lower-order terms in a bounded domain with Lipschitz boundary and frequent alternation of Dirichlet and Neumann conditions. Bibliography: 22 titles.
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Alkhutov et al. (2025) studied this question.
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