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.
Cite this article
Fabio Punzo, Alberto Tesei, Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, pp. 2001–2024DOI 10.1016/J.ANIHPC.2009.04.005