English

Accretivity of the general second order linear differential operator

Analysis of PDEs 2018-04-30 v1

Abstract

For the general second order linear differential operator L0=j,k=1najkjk+j=1nbjj+c\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 ajka_{jk}, bjb_{j}, and cc in an open set ΩRn\Omega \subseteq \mathbf{R}^n (n1n \ge 1), we present conditions which ensure that L0-\mathcal L_0 is accretive, i.e., ReL0ϕ,ϕ0{\rm Re} \, \langle -\mathcal L_0 \phi, \phi\rangle \ge 0 for all ϕC0(Ω).\phi \in C^\infty_0(\Omega).

Cite

@article{arxiv.1804.10326,
  title  = {Accretivity of the general second order linear differential operator},
  author = {V. G. Maz'ya and I. E. Verbitsky},
  journal= {arXiv preprint arXiv:1804.10326},
  year   = {2018}
}

Comments

24 pages

R2 v1 2026-06-23T01:37:38.142Z