Notions of Dirichlet problem for functions of least gradient in metric measure spaces
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2019
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en
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1603–1648
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Revista Matematica Iberoamericana, Volume 35, issue 6
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.Description
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Korte, R, Lahti, P, Shanmugalingam, N & Li, X 2019, ' Notions of Dirichlet problem for functions of least gradient in metric measure spaces ', Revista Matematica Iberoamericana, vol. 35, no. 6, pp. 1603–1648 . https://doi.org/10.4171/rmi/1095