We consider a general nonselfadjoint second order scalar operator in a planar domain such that one of the boundary components is obtained by an arbitrary irregular curving under the assumption that the curving amplitude is small. The Dirichlet or Neumann boundary condition is imposed on the perturbed boundary component, and the Dirichlet boundary condition is imposed on the remaining part of the boundary. We prove the norm resolvent convergence of operators, estimate the convergence rate in two operator norms, and prove the spectrum convergence of the perturbed operators. In the selfadjoint case, we establish the convergence of spectral projections.
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Translated from Problemy Matematicheskogo Analiza 116, 2022, pp. 69-84.
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Borisov, D.I. Operator Estimates for Planar Domains with Irregularly Curved Boundary. The Dirichlet and Neumann Conditions. J Math Sci 264, 562–580 (2022). https://doi.org/10.1007/s10958-022-06017-1
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DOI: https://doi.org/10.1007/s10958-022-06017-1