On nonequivalence of regular boundary points for second-order elliptic operators

N. V. Krylov, Timur Yastrzhembskiy

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In this paper, we present examples of nondivergence form of second-order elliptic operators with continuous coefficients, such that L has an irregular boundary point that is regular for the Laplacian. Also for any eigenvalue spread <1 of the matrix of the coefficients, we provide an example of operator with discontinuous coefficients that has regular boundary points nonequivalent to Laplacian’s (we give examples for each direction of nonequivalence). All examples are constructed for each dimension starting with 3.

Original languageEnglish (US)
Pages (from-to)366-387
Number of pages22
JournalCommunications in Partial Differential Equations
Issue number3
StatePublished - Mar 4 2017

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© 2017 Taylor & Francis.


  • Dirichlet problem
  • Wiener’s test
  • regular points


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