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.
Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients / F. Punzo, A. Tesei. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - 26:5(2009), pp. 2001-2024. [10.1016/j.anihpc.2009.04.005]
Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients
F. PunzoPrimo
;
2009
Abstract
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.
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