On nonequivalence of regular boundary points for second-order elliptic operators
Analysis of PDEs
2016-11-22 v3
Abstract
In this paper we present examples of nondivergence form second order elliptic operators with continuous coefficients such that 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.
Cite
@article{arxiv.1606.06346,
title = {On nonequivalence of regular boundary points for second-order elliptic operators},
author = {N. V. Krylov and Timur Yastrzhembskiy},
journal= {arXiv preprint arXiv:1606.06346},
year = {2016}
}
Comments
24 pages, added acknowledgment of Simons support, better historical remarks