Mathematics – Functional Analysis
Scientific paper
1993-03-26
Mathematics
Functional Analysis
19 pages
Scientific paper
Given an elliptic operator~$L$ on a bounded domain~$\Omega \subseteq {\bf R}^n$, and a positive Radon measure~$\mu$ on~$\Omega$, not charging polar sets, we discuss an explicit approximation procedure which leads to a sequence of domains~$\Omega_h \subseteq \Omega$ with the following property: for every~$f\in H^{-1}(\Omega)$ the sequence~$u_h$ of the solutions of the Dirichlet problems~$L\, u_h=f$ in~$\Omega_h$, $u_h=0$ on~$\partial \Omega_h$, extended to 0 in~$\Omega \setminus \Omega_h$, converges to the solution of the \lq\lq relaxed Dirichlet problem\rq\rq\ $L\,u+\mu u=f$ in~$\Omega$, $u=0$ on~$\partial \Omega$.
Malusa Annalisa
Maso Gianni Dal
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