Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators

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dc.contributor.authorHafeez, Usman
dc.contributor.authorLavier, Theo
dc.contributor.authorWilliams, Lucas
dc.contributor.authorKorobenko, Lyudmila
dc.date.accessioned2022-10-25T19:28:38Z
dc.date.available2022-10-25T19:28:38Z
dc.date.issued2021-09-23
dc.description.abstractWe investigate a connection between solvability of the Dirichlet problem for an infinitely degenerate elliptic operator and the validity of an Orlicz-Sobolev inequality in the associated subunit metric space. For subelliptic operators it is known that the classical Sobolev inequality is sufficient and almost necessary for the Dirichlet problem to be solvable with a quantitative bound on the solution [11]. When the degeneracy is of infinite type, a weaker Orlicz-Sobolev inequality seems to be the right substitute [7]. In this paper we investigate this connection further and reduce the gap between necessary and sufficient conditions for solvability of the Dirichlet problem.
dc.description.departmentMathematics
dc.formatText
dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationHafeez, U., Lavier, T., Williams, L., & Korobenko, L. (2021). Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators. <i>Electronic Journal of Differential Equations, 2021</i>(82), pp. 1-19.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16240
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectElliptic equations
dc.subjectInfinite degeneracy
dc.subjectRough coefficients
dc.subjectDirichlet problem
dc.subjectSolvability
dc.subjectGlobal boundedness
dc.subjectOrlicz-Sobolev inequality
dc.titleOrlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators
dc.typeArticle

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