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Part I: Green’s functions in singularly perturbed domains: Uniform asymptotic formulae for Green’s functions for the Laplacian in domains with small perforations |
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Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Green’s kernels |
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Green’s function for the Dirichlet boundary value problem in a domain with several inclusions |
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Numerical simulations based on the asymptotic approximations |
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Other examples of asymptotic approximations of Green’s functions in singularly perturbed domains |
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Part II: Green’s tensors for vector elasticity in bodies with small defects: Green’s tensor for the Dirichlet boundary value problem in a domain with a single inclusion |
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Green’s tensor in bodies with multiple rigid inclusions |
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Green’s tensor for the mixed boundary value problem in a domain with a small hole |
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Part III Meso-scale approximations. Asymptotic treatment of perforated domains without homogenization: Meso-scale approximations for solutions of Dirichlet problems |
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Mixed boundary value problems in multiply-perforated domains |
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Part I: Green’s functions in singularly perturbed domains: Uniform asymptotic formulae for Green’s functions for the Laplacian in domains with small perforations |
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Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Green’s kernels |
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Green’s function for the Dirichlet boundary value problem in a domain with several inclusions |
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