Accretivity of the general second order linear differential operator

Abstract

For the general second order linear differential operator $${\mathcal{L}}_0=\sum _{j,k=1}^n{a}_{jk}{\partial }_j{\partial }_k+\sum _{j=1}^n{b}_j{\partial }_j+c$$ with complex-valued distributional coefficients $a_{jk}$, $b_j$, and $c$ in an open set $\Omega \subseteq {\mathbf{R}}^n$ ($n\ge 1$), we present conditions which ensure that $-{\mathcal{L}}_0$ is accretive, i.e., $\mathrm{Re}⟨-{\mathcal{L}}_0\varphi ,\varphi ⟩\ge 0$ for all $\varphi \in C_0^{\infty }(\Omega ).$

24 pages

References in corpus (2)

• Infinitesimal form boundedness and Trudinger's subordination for the Schrödinger operator
• Global estimates for kernels of Neumann series and Green's functions