A simple characterization of H-convergence for a class of nonlocal problems

José C. Bellido*, Anton Evgrafov

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This is a follow-up of the paper J. Fernández-Bonder, A. Ritorto and A. Salort, H-convergence result for nonlocal elliptic-type problems via Tartar’s method, SIAM J. Math. Anal., 49 (2017), pp. 2387–2408, where the classical concept of H-convergence was extended to fractional p-Laplace type operators. In this short paper we provide an explicit characterization of this notion by demonstrating that the weak-∗ convergence of the coefficients is an equivalent condition for H-convergence of the sequence of nonlocal operators. This result takes advantage of nonlocality and is in stark contrast to the local p-Laplacian case.
Original languageEnglish
JournalRevista Matemática Complutense
ISSN1988-2807
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • Homogenization of nonlocal problems
  • H-convergenc
  • G-convergence

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