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We study a generalization of weighted Sobolev spaces associated to two weights and two exponents. We first give a criterion for the existence of an extension operator beyond the domain to the whole space and deduce that smooth functions up to the boundary of the domain form a dense open subset. By relying on this property, we then show the existence of a trace operator.

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A Trace Operator for Weighted Sobolev Spaces

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  • 发表日期：

    2025年

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  • Lucas Fresse,
  • Viorica V. Motreanu

摘要

We study a generalization of weighted Sobolev spaces associated to two weights and two exponents. We first give a criterion for the existence of an extension operator beyond the domain to the whole space and deduce that smooth functions up to the boundary of the domain form a dense open subset. By relying on this property, we then show the existence of a trace operator.