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A Trace Operator for Weighted Sobolev Spaces

In: Geometry and Non-Convex Optimization

Author

Listed:
  • Lucas Fresse

    (Université de Lorraine, Institut Élie Cartan)

  • Viorica V. Motreanu

    (Lycée Varoquaux)

Abstract

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.

Suggested Citation

  • Lucas Fresse & Viorica V. Motreanu, 2025. "A Trace Operator for Weighted Sobolev Spaces," Springer Optimization and Its Applications, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Geometry and Non-Convex Optimization, pages 101-119, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-87057-6_5
    DOI: 10.1007/978-3-031-87057-6_5
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