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<p>In this paper, we contribute to this growing body of research by studying a class of nonlinear anisotropic elliptic equations with drift terms, where both the diffusion and the lower-order terms exhibit non-standard directional growth. We aim to establish existence, regularity, and integrability results for weak or distributional solutions, even when the source term <i>f</i> belongs to a low Lebesgue space. This level of generality is essential for applications involving irregular data.</p>

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Generalisation of Stampachia-Caldéron Zygmund theory for anisotropic elliptic problems with drift terms

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Nour Elhouda Allaoui,
  • Fares Mokhtari

摘要

In this paper, we contribute to this growing body of research by studying a class of nonlinear anisotropic elliptic equations with drift terms, where both the diffusion and the lower-order terms exhibit non-standard directional growth. We aim to establish existence, regularity, and integrability results for weak or distributional solutions, even when the source term f belongs to a low Lebesgue space. This level of generality is essential for applications involving irregular data.