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<p>We establish the existence of nontrivial and distinct weak solutions to a singular <i>p</i>–Laplacian elliptic equation in a smooth bounded domain with Dirichlet boundary condition. The result is obtained through limits of sequences of solutions to an auxiliary equation. To this end, we derive local and weak gradient estimates.</p>

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Solutions for a singular quasilinear elliptic equation

  • 期刊论文

  • 发表日期：

    2025年9月19日

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  • Eduardo Hitomi,
  • Marcelo Montenegro

摘要

We establish the existence of nontrivial and distinct weak solutions to a singular p–Laplacian elliptic equation in a smooth bounded domain with Dirichlet boundary condition. The result is obtained through limits of sequences of solutions to an auxiliary equation. To this end, we derive local and weak gradient estimates.