Domain Perturbation for Linear and Semi-Linear Boundary Value Problems
作者： Daniel Daners
DOI: 10.1016/S1874-5733(08)80018-6
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摘要: Abstract This is a survey on elliptic boundary value problems varying domains and tools needed for that. Such arise in numerical analysis, shape optimisation the investigation of solution structure nonlinear equations. The methods are also useful to obtain certain results equations non-smooth by approximation smooth domains. Domain independent estimates smoothing properties an essential tool deal with domain perturbation problems, especially non-linear Hence we discuss such extensively, together some abstract linear operators. A second major part deals specific various conditions. We completely characterise convergence Dirichlet conditions give simple sufficient then prove homogenisation Robin fast oscillating boundaries, where condition changes limit. finally mention Neumann final concerned about using Leray-Schauder degree existence solutions slightly perturbed demonstrate how use get unbounded
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