Mathematica Eterna
Open Access

Abstract

Global boundedness for solutions to some anisotropic elliptic systems

Guo Meiqi and Gao Hongya

This paper deals with anisotropic solutions u ∈ u∗+W 1,(pi) 0 (w, Ω, R N ) to the nonlinear elliptic system − Xn i=1 Di(a α i (x, Du(x))) = 0, α = 1, · · · , N. We present a monotonicity inequality on the matrix a = (a α i ) ∈ R N×n with weight, which guarantees global pointwise bounds for the anisotropic solutions u with gradient constraint.