Results of ω-order reversing partial contraction mapping generating a differential operator

Abstract

In this paper, we presents some partial differential operators defined on suitably chosen function spaces such as H^{−1}(Ω), L^{p}(Ω), with p∈[1,+∞). Laplace operator on a domain Ω in R^{n} subject to the Dirichlet boundary condition was established by generating a C_0-semigroup, which is generated by an infinitesimal generator ω-order reversing partial contraction (ω-ORCP_n).