ISSN: 1314-3344
+44-77-2385-9429
Guo Kaili and Gao Hongya
In this paper we consider the minimum principle for vector valued minimizers of some functionals F(u; Ω) = Z Ω f(x, Du(x))dx. The main assumption on the density f(x, z)is a kind of ”monotonicity” with respect to the N × n matrix z. We also consider the maximum and minimum principle for weak solutions u of some elliptic systems − Xn i=1 Di(a α i (x, u(x)) = 0, x ∈ Ω, α = 1, . . . , N, and the main assumption on a α i (x, z) is 0 < Xn j=1 X N α=1 a α i (x, z)(z α i − z˜ α i ), where ˜z is a N × n matrix with respect to z.