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 editors: Korte, Riikka; Lahti, Panu; Li, Xining; Shanmugalingam, Nageswari

Journal or series: Revista Matematica Iberoamericana

ISSN: 0213-2230

eISSN: 2235-0616

Publication year: 2019

Volume: 35

Issue number: 6

Pages range: 1603-1648

Publisher: European Mathematical Society Publishing House

Publication language: English

DOI: https://doi.org/10.4171/rmi/1095

Publication open access: Not 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

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.

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

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2019

JUFO rating: 2