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<p>We study the Dirichlet problem for an elliptic equation with the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$ p(|x|) $</EquationSource> </InlineEquation>-Laplacian and lower-order terms that do not satisfy the Bernstein–Nagumo condition.Under the assumption that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$ p(|x|) $</EquationSource> </InlineEquation> is a&#xa0;continuously differentiable nonincreasing function, we prove the existence of a weak radially symmetric solution whose derivative is Hölder continuous.</p>

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On Radially Symmetric Solutions to the Dirichlet Problem for an Elliptic Equation with the \( p(|x|) \)-Laplacian

  • 期刊论文

  • 发表日期：

    2026年3月28日

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  • Ar. S. Tersenov,
  • R. Ch. Safarov

摘要

We study the Dirichlet problem for an elliptic equation with the $ p(|x|) $ -Laplacian and lower-order terms that do not satisfy the Bernstein–Nagumo condition.Under the assumption that $ p(|x|) $ is a continuously differentiable nonincreasing function, we prove the existence of a weak radially symmetric solution whose derivative is Hölder continuous.