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Singular perturbations in \(L_ p\). (English) Zbl 0656.35008

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 \((\epsilon A+B)u=f\).

MSC:

35B25 Singular perturbations in context of PDEs
35J40 Boundary value problems for higher-order elliptic equations
35C20 Asymptotic expansions of solutions to PDEs
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