Accretivity of the General Second Order Linear Differential Operator

Abstract

For the general second order linear differential operatorL0=∑j,k=1najk∂j∂k+∑j=1nbj∂j+c with complex-valued distributional coefficients a j,k , b j , and c in an open set Ω ⊆ ℝ n (n ≥ 1), we present conditions which ensure that −L is accretive, i.e., Re ⟨−Lϕ, ϕ⟩≥0 for all φ ∈ C 0 ∞ (Ω). © 2019, Springer-Verlag GmbH Germany & The Editorial Office of AMS