Scholarlink

<p>We prove the existence and uniform boundedness of weak solutions to a nonlinear elliptic boundary value problem in Orlicz–Sobolev spaces. The problem features a nonstandard growth condition and a general nonlinearity that depends on both the solution and its gradient through an intrinsic operator. Using truncation methods and Moser iteration techniques, we prove the existence of solutions and establish uniform <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^\infty \)</EquationSource> </InlineEquation>-bounds independent of the truncation parameter. Our results generalize previous work on problems with polynomial growth to the more general Orlicz–Sobolev framework.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Existence and Boundedness of Solutions for a Nonlinear Elliptic Problem in Orlicz–Sobolev Spaces

  • 期刊论文

  • 发表日期：

    2025年9月23日

查看全文
  • Fatemeh Mafi,
  • Abdolrahman Razani

摘要

We prove the existence and uniform boundedness of weak solutions to a nonlinear elliptic boundary value problem in Orlicz–Sobolev spaces. The problem features a nonstandard growth condition and a general nonlinearity that depends on both the solution and its gradient through an intrinsic operator. Using truncation methods and Moser iteration techniques, we prove the existence of solutions and establish uniform \(L^\infty \) -bounds independent of the truncation parameter. Our results generalize previous work on problems with polynomial growth to the more general Orlicz–Sobolev framework.