A class of integral functionals with a -minimum

  • David Arcoya

    Universidad de Granada, Spain
  • Lucio Boccardo

    Istituto Lombardo, Milano; Sapienza Università di Roma, Italy
A class of integral functionals with a $W^{1,1}_0$-minimum cover

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Abstract

In this paper, we study the minimization of the integral functionals of the type

where , , , and . The degeneracy of the principal part of the functional implies that it is not coercive in and pushes to set and solve the minimization problem in instead of the space . In addition, when the coefficients and are merely in , but satisfy for some the condition , we show the existence of a minimum of the functional which belongs to .

Cite this article

David Arcoya, Lucio Boccardo, A class of integral functionals with a -minimum. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 3, pp. 535–551

DOI 10.4171/RLM/979