A1 Journal article (refereed)
Notions of Dirichlet problem for functions of least gradient in metric measure spaces (2019)

Korte, R., Lahti, P., Li, X., & Shanmugalingam, N. (2019). Notions of Dirichlet problem for functions of least gradient in metric measure spaces. Revista Matematica Iberoamericana, 35(6), 1603-1648. https://doi.org/10.4171/rmi/1095

JYU authors or editors

Publication details

All authors or editorsKorte, Riikka; Lahti, Panu; Li, Xining; Shanmugalingam, Nageswari

Journal or seriesRevista Matematica Iberoamericana



Publication year2019


Issue number6

Pages range1603-1648

PublisherEuropean Mathematical Society Publishing House

Publication languageEnglish


Publication open accessNot open

Publication channel open access

Publication is parallel published (JYX)https://jyx.jyu.fi/handle/123456789/66330

Web address of parallel published publication (pre-print)https://arxiv.org/abs/1612.06078


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.

Free keywordsfunction of bounded variation; inner trace; perimeter; least gradient; p-harmonic; Dirichlet problem; metric measure space; Poincaré inequality; codimension 1 Hausdorff measure

Contributing organizations

Ministry reportingYes

Reporting Year2019

JUFO rating2

Last updated on 2024-11-05 at 22:05