Abstract

We study the relaxation of a degenerate functional with linear growth, depending on a weight w that does not exhibit doubling or Muckenhoupt-type conditions. In order to obtain an explicit representation of the relaxed functional and its domain, our main tools for are Sobolev inequalities with double weight.

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Keywords

  • Lower semicontinuity
  • relaxation
  • degenerate variational integrals
  • weight
  • Poincaré inequality

Mathematics Subject Classification

26A15, 49J45

Suggested citation

V. Chiadò Piat, V. De Cicco, A. Melchor Hernandez. “Relaxation for a Degenerate Functional with Linear Growth in the Onedimensional Case.” Journal of Convex Analysis 33 (2026), No. 1&2, 335–360. https://doi.org/10.68381/jca33021

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.