We study well-posedness of the Dirichlet problem for linear degenerate elliptic equations under mild assumptions on the coefficients (in particular, they can be unbounded). We provide sufficient conditions both for uniqueness and nonuniqueness of solutions, which rely on the construction of suitable sub- and supersolutions to certain auxiliary problems. © 2009 Elsevier Masson SAS. All rights reserved.
Punzo, F., & Tesei, A. (2009). Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, 26(5), 2001–2024. https://doi.org/10.1016/j.anihpc.2009.04.005