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We study interpolation properties of the perturbed Sobolev spaces \(H^{s,p}_\alpha \) , associated with singular perturbation \(\Delta _\alpha \) of Laplace operator in Euclidean space of dimensions 2 and 3. The interpolation result implies interpolation inequalities useful in the applications.

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Interpolation of Sobolev Spaces for Laplace Operator with Contact Interaction

  • 会议论文

  • 发表日期：

    2025年

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  • Vladimir Georgiev,
  • Mario Rastrelli

摘要

We study interpolation properties of the perturbed Sobolev spaces \(H^{s,p}_\alpha \) , associated with singular perturbation \(\Delta _\alpha \) of Laplace operator in Euclidean space of dimensions 2 and 3. The interpolation result implies interpolation inequalities useful in the applications.