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On the Boyarsky–Meyers Estimate for the Gradient of the Solution to the Dirichlet Problem for a Second-Order Linear Elliptic Equation with Drift: The Case of Critical Sobolev Exponent

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Abstract

Increased integrability of the gradient of the solution to the homogeneous Dirichlet problem for the Poisson equation with lower terms in a bounded Lipschitz domain is established. The unique solvability of this problem is also proved.

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Funding

The results of this work were obtained as part of the state  assignment at Vladimir State University, project no. FZUN-2023-0004.

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Correspondence to Yu. A. Alkhutov or A. G. Chechkina.

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The authors of this work declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Alkhutov, Y.A., Chechkina, A.G. On the Boyarsky–Meyers Estimate for the Gradient of the Solution to the Dirichlet Problem for a Second-Order Linear Elliptic Equation with Drift: The Case of Critical Sobolev Exponent. Dokl. Math. 109, 170–174 (2024). https://doi.org/10.1134/S1064562424701990

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  • DOI: https://doi.org/10.1134/S1064562424701990

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