JournalsrlmVol. 33, No. 4pp. 757–794

A note on BV and 1-Sobolev functions on the weighted Euclidean space

  • Maria Stella Gelli

    Università di Pisa, Italy

  • Danka Lučić

    Università di Pisa, Italy
A note on BV and 1-Sobolev functions on the weighted Euclidean space cover
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Abstract

In the setting of the Euclidean space equipped with an arbitrary Radon measure, we prove the equivalence between several notions of function of bounded variation present in the literature. We also study the relation between various definitions of 1-Sobolev function.

Cite this article

Maria Stella Gelli, Danka Lučić, A note on BV and 1-Sobolev functions on the weighted Euclidean space. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 33 (2022), no. 4, pp. 757–794

DOI 10.4171/RLM/988