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<p>We present a sufficient condition, expressed in terms of Wolff potentials, for the existence of a finite energy solution to the measure data (<i>p</i>,&#xa0;<i>q</i>)-Laplacian equation with a “sublinear growth” rate. Furthermore, we prove that such a solution is minimal. Additionally, a lower bound of a suitably generalized Wolff-type potential is necessary for the existence of a solution, even if the energy is not finite. Our main tools include integral inequalities closely associated with (<i>p</i>,&#xa0;<i>q</i>)-Laplacian equations with measure data and pointwise potential estimates, which are crucial for establishing the existence of solutions to this type of problem. This method also enables us to address other nonlinear elliptic problems involving a general class of quasilinear operators.</p>

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Finite Energy Solutions of Quasilinear Elliptic Equations with Orlicz Growth

  • 期刊论文

  • 发表日期：

    2025年4月10日

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  • Estevan Luiz da Silva,
  • João Marcos do Ó

摘要

We present a sufficient condition, expressed in terms of Wolff potentials, for the existence of a finite energy solution to the measure data (p, q)-Laplacian equation with a “sublinear growth” rate. Furthermore, we prove that such a solution is minimal. Additionally, a lower bound of a suitably generalized Wolff-type potential is necessary for the existence of a solution, even if the energy is not finite. Our main tools include integral inequalities closely associated with (p, q)-Laplacian equations with measure data and pointwise potential estimates, which are crucial for establishing the existence of solutions to this type of problem. This method also enables us to address other nonlinear elliptic problems involving a general class of quasilinear operators.