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<p>We establish that a generalized Hölder continuous function on an (<i>m</i> − 2)-Ahlfors regular compact set in ℝ<sup><i>m</i></sup> can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function.</p>

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Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月6日

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  • Grigori Rozenblum,
  • Nikolai Shirokov

摘要

We establish that a generalized Hölder continuous function on an (m − 2)-Ahlfors regular compact set in ℝm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function.