Geodesic
Limits of Sobolev homeomorphisms
Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 473-505

Voir la notice de l'article provenant de la source EMS Press

Let X,Y∈R2 be topologically equivalent bounded Lipschitz domains. We prove that weak and strong limits of homeomorphisms h:X⟶onto​Y in the Sobolev space W1,p(X,R2),p≥2, are the same. As an application, we establish the existence of 2D-traction free minimal deformations for fairly general energy integrals.
DOI : 10.4171/jems/671
Classification : 30-XX, 46-XX, 58-XX
Keywords: Energy-minimal deformations, approximation of Sobolev homeomorphisms, variational integrals, harmonic mappings, p-harmonic equation 
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     author = {Tadeusz Iwaniec and Jani Onninen},
     title = {Limits of {Sobolev} homeomorphisms},
     journal = {Journal of the European Mathematical Society},
     pages = {473--505},
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     year = {2017},
     doi = {10.4171/jems/671},
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Tadeusz Iwaniec; Jani Onninen. Limits of Sobolev homeomorphisms. Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 473-505. doi: 10.4171/jems/671

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