Unicité des solutions du type Kruskov pour des problèmes elliptiques avec des termes de transport nonlinéaires. (Uniqueness of the Kruskov solution of elliptic problems with nonlinear convexion). (French) Zbl 0623.35030

Carrillo, José

C. R. Acad. Sci., Paris, Sér. I 303, 189 (1986).

We prove uniqueness of Kruskov solution of the equation \[ -\Delta u+div(\beta (u))+au\ni f\geq 0 \] with homogeneous boundary datum. \(\beta\) is not necessarily continuous.

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
49Q05	Minimal surfaces and optimization
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35R05	PDEs with low regular coefficients and/or low regular data

Keywords:

uniqueness; Kruskov solution; homogeneous boundary datum