Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients
Luigi Negro, Chiara Spina · Forum Mathematicum · 2019
Abstract We study the behaviour at infinity, in suitable weighted L p {L^{p}} -norms, of solutions of parabolic problems associated to the second order elliptic operator L = Δ + ( a - 1 ) ∑ i , j = 1 N x i x j | x | 2 D i j + c x | x | 2 ⋅ ∇ - b | x | - 2 , L=\Delta+(a-1)\sum_{i,j=1}^{N}\frac{x_{i}x_{j}}{|x|^{2}}D_{ij}+c\frac{x}{|x|^{% 2}}\cdot abla-b|x|^{-2}, where a > 0 {a>0} and b , c ∈ ℝ {b,c\in\mathbb{R}} .