On nonequivalence of regular boundary points for second-order elliptic operators. Issue 3 (4th March 2017)

• Record Type: Journal Article
• Authors: Krylov, N. V.; Yastrzhembskiy, Timur
• Is Part Of: Communications in partial differential equations. Volume 42:Issue 3(2017)
• Page Start: 366
• Page End: 387
• Publication Date: 2017-03-04
• Subjects: Dirichlet problem -- regular points -- Wiener's test; 35J25 -- 35J67; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2017.1278771
• Languages: English
• ISSNs: 0360-5302

Abstract

ABSTRACT: 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.