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- W2101775900 abstract "This paper features a class of mappings h = ( h 1 , … , h m ) : 𝕏 → onto 𝕐 between bounded domains 𝕏, 𝕐 ⊂ ℝn, having finite n-harmonic energy, such that we have E [ h ] = ∫ X ‖ D h ( x ) ‖ n d x , ‖ D h ‖ 2 = Tr ( D * h D h ) . The fundamental question is whether or not the domains 𝕏, 𝕐 ⊂ ℝn of the same topological type admit a homeomorphism h : X → onto Y in a given homotopy class having finite energy. The examples of non-existence, somewhat testing our theory, arise when we remove from bounded smooth domains 𝕏 and 𝕐 thin subsets X ⊂ X and Υ ⊂ Y , referred to as cracks or fractures. We are looking for homeomorphisms h : X X → onto Y ϒ of finite energy for which ϒ is the cluster set of h over X. In general, infinite energy is required in order to increase the dimension of a crack X ⊂ X that is, when X < dim Υ ⩽ n − 1. Suppose now that a bounded deformation h : X ∖ X → R n of finite energy is given. Does h extend continuously to 𝕏 and, if so, is the extension injective on 𝕏? We give affirmative answers to these questions." @default.
- W2101775900 created "2016-06-24" @default.
- W2101775900 creator A5063970255 @default.
- W2101775900 creator A5064887197 @default.
- W2101775900 date "2009-05-14" @default.
- W2101775900 modified "2023-09-23" @default.
- W2101775900 title "Deformations of finite conformal energy: existence and removability of singularities" @default.
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- W2101775900 doi "https://doi.org/10.1112/plms/pdp016" @default.
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