Notions of Dirichlet problem for functions of least gradient in metric measure spaces

Riikka Korte, Panu Lahti, Nageswari Shanmugalingam, Xining Li

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
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Abstract

We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p-harmonic functions, p>1, and letting p→1. Tools developed and used in this paper include the inner perimeter measure of a domain.
Original languageEnglish
Pages (from-to)1603–1648
JournalRevista Matematica Iberoamericana
Volume35
Issue number6
DOIs
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed

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