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<p>In this work, we study a nonlinear elliptic problem associated with a differential inclusion involving degenerate coercivity and subject to a Neumann boundary condition. The model problem consists of an elliptic operator of <i>p</i>-Laplacian type with a degeneration depending on the unknown function and a maximal monotone graph. The domain is bounded with smooth boundary. We establish the existence of a bounded weak solution for essentially bounded data. We also prove the existence of entropy solutions for integrable data and obtain additional regularity properties.</p>

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Weak and entropy solutions for nonlinear multivalued elliptic problems with degenerate coercivity and homogeneous Neumann boundary condition

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Morad Ouboufettal,
  • Mohammed El Ansari,
  • Youssef Akdim

摘要

In this work, we study a nonlinear elliptic problem associated with a differential inclusion involving degenerate coercivity and subject to a Neumann boundary condition. The model problem consists of an elliptic operator of p-Laplacian type with a degeneration depending on the unknown function and a maximal monotone graph. The domain is bounded with smooth boundary. We establish the existence of a bounded weak solution for essentially bounded data. We also prove the existence of entropy solutions for integrable data and obtain additional regularity properties.