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Existence of solutions to a general geometric elliptic variational problem

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dc.abstract.enWe consider the problem of minimising an inhomogeneous anisotropic elliptic functional in a class of closed m dimensional subsets of R n which is stable under taking smooth deformations homotopic to the identity and under local Hausdorff limits. We prove that the minimiser exists inside the class and is an ( H m , m) rectifiable set in the sense of Federer. The class of competitors encodes a notion of spanning a boundary. We admit unrectifiable and non-compact competitors and boundaries, and we make no restrictions on the dimension m and the co-dimension n − m other than 1 ≤ m < n. An important tool for the proof is a novel smooth deformation theorem. The skeleton of the proof and the main ideas follow Almgren’s (Ann Math (2) 87:321–391, 1968) paper. In the end we show that classes of sets spanning some closed set B in homological and cohomological sense satisfy our axioms.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorKolasiński, Sławomir
dc.contributor.authorFang, Yangqin
dc.date.accessioned2024-01-25T00:07:01Z
dc.date.available2024-01-25T00:07:01Z
dc.date.issued2018
dc.description.financeNie dotyczy
dc.description.number3
dc.description.volume57
dc.identifier.doi10.1007/S00526-018-1348-4
dc.identifier.issn0944-2669
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/106713
dc.identifier.weblinkhttps://doi.org/10.1007/s00526-018-1348-4
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofCalculus of Variations and Partial Differential Equations
dc.relation.pages91:1-91:71
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enthe Plateau problem
dc.subject.enanisotropic functional
dc.subject.envarifold
dc.subject.enellipticity in geometric variational problems
dc.titleExistence of solutions to a general geometric elliptic variational problem
dc.typeJournalArticle
dspace.entity.typePublication