Results of $\omega$-order reversing partial contraction mapping generating a differential operator
Akinola Yussuff Akinyele, J. U. Abubakar, Kareem Akanbi Bello, iman Kinbokun Alhassan, Moses Adebowale Aasa · Malaya Journal of Matematik · 2022
In this paper, we presents some partial differential operators defined on suitably chosen function spaces such as \(H^{-1}(\Omega)\), \(L^{p}(\Omega)\), with \(p \in [1,+\infty)\). Laplace operator on a domain \(\Omega \in \mathbb{R}^{n}\) subject to the Dirichlet boundary condition was established by generating a \(C_{0}\)-semigroup, which is generated by an infinitesimal generator \(\omega\)-order reversing partial contraction (\(\omega\)-\(ORCP_n\)).