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dc.contributor.authorLancaster, Kirk E.
dc.contributor.authorMelin, Jaron Patric
dc.identifier.citationLancaster, Kirk E.; Melin, Jaron Patric. 2016. On the relationship of continuity and boundary regularity in prescribed mean curvature dirichlet problems. Pacific Journal of Mathematics, vol. 282:No. 2:pp 415–436en_US
dc.descriptionClick on the DOI link to access the article (may not be free).en_US
dc.description.abstractIn 1976, Leon Simon showed that if a compact subset of the boundary of a domain is smooth and has negative mean curvature, then the nonparametric least area problem with Lipschitz continuous Dirichlet boundary data has a generalized solution which is continuous on the union of the domain and this compact subset of the boundary, even if the generalized solution does not take on the prescribed boundary data. Simon's result has been extended to boundary value problems for prescribed mean curvature equations by other authors. In this note, we construct Dirichlet problems in domains with corners and demonstrate that the variational solutions of these Dirichlet problems are discontinuous at the corner, showing that Simon's assumption of regularity of the boundary of the domain is essential.en_US
dc.publisherPacific Journal of Mathematicsen_US
dc.relation.ispartofseriesPacific Journal of Mathematics;vol.282:no.2
dc.subjectPrescribed mean curvatureen_US
dc.subjectNonconvex corneren_US
dc.subjectDirichlet problemen_US
dc.titleOn the relationship of continuity and boundary regularity in prescribed mean curvature dirichlet problemsen_US
dc.rights.holder© 2016 Pacific Journal of Mathematics. All rights reserved.en_US

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