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      Diffeomorphic approximation of Sobolev homeomorphisms

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          Abstract

          Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.

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          Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity

          J M Ball (1982)
          Article 0 comments Cited 79 times – based on 0 reviews     Review now
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            Global invertibility of Sobolev functions and the interpenetration of matter

            J M Ball (1981)
            A global inverse function theorem is established for mappingsu: Ω → ℝn, Ω ⊂ ℝnbounded and open, belonging to the Sobolev spaceW1.p(Ω),p>n. The theorem is applied to the pure displacement boundary value problem of nonlinear elastostatics, the conclusion being that there is no interpenetration of matter for the energy-minimizing displacement field.
            Article 0 comments Cited 58 times – based on 0 reviews     Review now
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              Regularity properties of deformations with finite energy

              Vladimir Sverak (1988)
              Article 0 comments Cited 40 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Publication date Created: 01 September 2010
                Article
                DOI: 10.1007/s00205-011-0404-4
                ArXiV ID: 1009.0286
                SO-VID: b0983d43-c534-4812-b99f-c0b741eba9c6
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                ACM classes 46E35, 30E10, 35J92
                Journal reference Arch. Rat. Mech. Anal. 201 (2011), no. 3, 1047-1067
                Comments 21 pages, 5 figures
                Categories math.AP math.CV

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