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<p>This paper derives a local boundedness result with anisotropic Caccioppoli inequality by using De Giorgi’s iteration method. As applications, we first consider elliptic equations, under some anisotropic growth conditions, we derive that the solutions are locally bounded; secondly, we consider a nonlinear elliptic system in divergence form, satisfying anisotropic growth conditions, and derive local boundedness of weak solutions.</p>

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Local boundedness under anisotropic growth conditions

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Zesheng Feng,
  • Aiping Zhang,
  • Hongya Gao

摘要

This paper derives a local boundedness result with anisotropic Caccioppoli inequality by using De Giorgi’s iteration method. As applications, we first consider elliptic equations, under some anisotropic growth conditions, we derive that the solutions are locally bounded; secondly, we consider a nonlinear elliptic system in divergence form, satisfying anisotropic growth conditions, and derive local boundedness of weak solutions.