Notions of Dirichlet problem for functions of least gradient in metric measure spaces
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
Julkaistu sarjassaRevista Matematica Iberoamericana
© 2019 European Mathematical Society
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.
JulkaisijaEuropean Mathematical Society Publishing House
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Lisätietoja rahoituksestaR. Korte was supported by Academy of Finland grant number 308063, P. Lahti was supported by a grant from the Finnish Cultural Foundation, and X. Li was supported by NNSF of China (No. 11701582). The research of N. Shanmugalingam is partially supported by the grant # DMS–1500440 of NSF (USA).
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