6533b872fe1ef96bd12d308d

RESEARCH PRODUCT

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

Xining LiRiikka KorteNageswari ShanmugalingamPanu Lahti

subject

Pure mathematicsGeneral MathematicsPoincaré inequalitycodimension 1 Hausdorff measure01 natural sciencesMeasure (mathematics)symbols.namesakeMathematics - Analysis of PDEsMathematics - Metric GeometryFOS: Mathematicsinner trace0101 mathematicsleast gradientMathematicsDirichlet problemDirichlet problemp-harmonicDirect method010102 general mathematicsA domainMetric Geometry (math.MG)perimeterfunction of bounded variationmetric measure spacePoincaré inequalityBounded functionMetric (mathematics)symbolsAnalysis of PDEs (math.AP)

description

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. Peer reviewed

yearjournalcountryeditionlanguage
2019-01-01
http://urn.fi/URN:NBN:fi:jyu-201911124839