In this note we present some uniqueness and comparison results for a class of problem of the form. (0.1)-Lu=H(x,u,∇;u)+h(x),u∈H01(Ω)∩L∞(Ω), where Ω⊂RN, N≥. 2 is a bounded domain, L is a general elliptic second order linear operator with bounded coefficients and H is allowed to have a critical growth in the gradient. In some cases our assumptions prove to be sharp.
- Quadratic growth in the gradient
- Quasilinear elliptic equations
- Uniqueness of solution
ASJC Scopus subject areas
- Applied Mathematics