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Title: On the resolvent of multidimensional operators with frequently changing boundary conditions in the case of the homogenized Dirichlet condition

We consider an elliptic operator in a multidimensional domain with frequently changing boundary conditions in the case when the homogenized operator contains the Dirichlet boundary condition. We prove the uniform resolvent convergence of the perturbed operator to the homogenized operator and obtain estimates for the rate of convergence. A complete asymptotic expansion is constructed for the resolvent when it acts on sufficiently smooth functions. Bibliography: 41 titles.
Authors:
 [1]
  1. Bashkir State Pedagogical University, Ufa (Russian Federation)
Publication Date:
OSTI Identifier:
22364689
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; BOUNDARY CONDITIONS; CONVERGENCE; DIRICHLET PROBLEM; FUNCTIONS; MATHEMATICAL OPERATORS