On the weak differentiability of u o f-1

• Autores: Stanislav Henci
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 107, Nº 2, 2010, págs. 198-208
• Idioma: inglés
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• Resumen

  • Let p≥n−1 and suppose that f:Ω→Rn is a homeomorphism in the Sobolev space W1,p(loc(Ω,Rn). Further let u∈W1,q(loc(Ω) where q=pp−(n−1) and for q>n we also assume that u is continuous. Then u∘f−1∈(BV(loc(f(Ω)) and if we moreover assume that f is a mapping of finite distortion, then u∘f−1∈W1,1(loc(f(Ω)).