Najman, B. Singular perturbations in \(L_ p\). (English) Zbl 0656.35008 Glas. Mat., III. Ser. 22(42), No. 1, 25-51 (1987). We prove the a priori \(L_ p\)-estimates for the operator \(\epsilon A+B\) where A and B are Dirichlet elliptic operators of order 2m and \(2m'\) \((m>m')\). This estimate yields the optimal convergence rate for the solutions \(u_{\epsilon}\) of the problem \((\epsilon A+B)u=f\). Cited in 1 ReviewCited in 1 Document MSC: 35B25 Singular perturbations in context of PDEs 35J40 Boundary value problems for higher-order elliptic equations 35C20 Asymptotic expansions of solutions to PDEs Keywords:a priori \(L_ p\)-estimates; Dirichlet elliptic operators; order 2m; optimal convergence rate PDFBibTeX XMLCite \textit{B. Najman}, Glas. Mat., III. Ser. 22(42), No. 1, 25--51 (1987; Zbl 0656.35008)