TOPICS ON THE RESOLVENT OF
NON-SELF-ADJOINT ELLIPTIC DIFFERENTIAL OPERATORS
Reza Shokri Alvar1, Ali Sameripour2
1,2 Mathematics Dept., Lorestan University
Khoramabad, IRAN

Abstract

Let $\Omega \subset R^{n}$ be a bounded domain with smooth boundary $\partial\Omega \in C^{\infty}$. In this paper, we consider the linear operator

\begin{displaymath}(Pu)(x)=-\sum\limits_{i,j=1}^{n}{\frac{\partial }{\partial {{... ...}_{ij}}(x)Q(x)\frac{\partial u(x)}{\partial {{x}_{i}}} \right),\end{displaymath}

in the space $H_{\ell}=L^{2}(\Omega)^{\ell}=L^{2}(\Omega) \times \cdots \times L^{2}(\Omega)$ ($\ell$-times) associated with the noncoercive bilinear form that defined by

\begin{displaymath}{\cal P}[u,v]={{\sum\nolimits_{i,j=1}^{n}{\int_{\Omega }{\lef... ...rtial {{x}_{j}}} \right\rangle }}}_{{{\mathbf{C}}^{\ell }}}}dx.\end{displaymath}

In view of our ealier paper (see [10]), let the conditions made on the weighted function $\omega(x)$ be sufficiently more general than [10]. In this paper we investigate the resolvent of the operator $P$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 5
Year: 2021

DOI: 10.12732/ijam.v34i5.3

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