Journal of Convex Analysis 33 (2026), No. 1&2, 335--360
Copyright Heldermann Verlag 2026
Relaxation for a Degenerate Functional with Linear Growth in the Onedimensional Case
Valeria Chiado Piat
Dip. di Scienze Matematiche "G. Lagrange", Politecnico di Torino, Torino, Italy
valeria.chiadopiat@polito.it
Virginia De Cicco
Dip. di Scienze di Base e Applicate per l'Ingegneria, Università "La Sapienza", Roma, Italy
virginia.decicco@uniroma1.it
Anderson Melchor Hernandez
Dip. di Matematica, Università di Bologna, Bologna, Italy
anderson.melchor@unibo.it
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.
Keywords: Lower semicontinuity, relaxation, degenerate variational integrals, weight, Poincare inequality.
MSC: 26A15, 49J45.
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