The planar Least Gradient problem in convex domains, the case of continuous datum

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dc.contributor.authorRybka, Piotr
dc.contributor.authorSabra, Ahmad
dc.contributor.departmentDepartment of Mathematics
dc.contributor.facultyFaculty of Arts and Sciences (FAS)
dc.contributor.institutionAmerican University of Beirut
dc.date.accessioned2025-01-24T11:24:42Z
dc.date.available2025-01-24T11:24:42Z
dc.date.issued2022
dc.description.abstractWe study the two dimensional least gradient problem in a convex polygonal set in the plane. We show existence of solutions when the boundary data are attained in the trace sense. Due to the lack of strict convexity, the classical results are not applicable. We state the admissibility conditions on the continuous boundary datum f that are sufficient for establishing an existence and uniqueness result. The solutions are constructed by a limiting process, which uses the well-known geometry of superlevel sets of least gradient functions. © 2021 Elsevier Ltd
dc.identifier.doihttps://doi.org/10.1016/j.na.2021.112595
dc.identifier.eid2-s2.0-85116078621
dc.identifier.urihttp://hdl.handle.net/10938/26098
dc.language.isoen
dc.publisherElsevier Ltd
dc.relation.ispartofNonlinear Analysis, Theory, Methods and Applications
dc.sourceScopus
dc.subjectBv functions
dc.subjectConvex but not strictly convex domains
dc.subjectLeast gradient
dc.subjectTrace solutions
dc.subjectBoundary data
dc.subjectContinuous data
dc.subjectConvex but not strictly convex domain
dc.subjectConvex domains
dc.subjectExistence of solutions
dc.subjectStrictly convexes
dc.subjectTrace solution
dc.subjectTwo-dimensional
dc.subjectNonlinear analysis
dc.titleThe planar Least Gradient problem in convex domains, the case of continuous datum
dc.typeArticle

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