weak differentiability
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2020 ◽  
Vol 368 ◽  
pp. 107144 ◽  
Author(s):  
João P.G. Ramos ◽  
Olli Saari ◽  
Julian Weigt

2018 ◽  
Vol 149 ◽  
pp. 23-65 ◽  
Author(s):  
Dorival Leão ◽  
Alberto Ohashi ◽  
Alexandre B. Simas

2015 ◽  
Vol 13 (5) ◽  
pp. 2801-2811
Author(s):  
Sokol Bush Kaliaj

2015 ◽  
Vol 35 (6) ◽  
pp. 2405-2421 ◽  
Author(s):  
Martin Brokate ◽  
◽  
Pavel Krejčí ◽  

2010 ◽  
Vol 107 (2) ◽  
pp. 198 ◽  
Author(s):  
Stanislav Hencl

Let $p\geq n-1$ and suppose that $f:\Omega\to{\mathsf R}^n$ is a homeomorphism in the Sobolev space $W^{1,p}_{(\mathrm{loc}}(\Omega,{\mathsf R}^n)$. Further let $u\in W^{1,q}_{(\mathrm{loc}}(\Omega)$ where $q=\frac{p}{p-(n-1)}$ and for $q>n$ we also assume that $u$ is continuous. Then $u\circ f^{-1}\in (\mathrm{BV}_{(\mathrm{loc}}(f(\Omega))$ and if we moreover assume that $f$ is a mapping of finite distortion, then $u\circ f^{-1}\in W^{1,1}_{(\mathrm{loc}}(f(\Omega))$.


2010 ◽  
Vol 35 (1) ◽  
pp. 27-51 ◽  
Author(s):  
Bernd Heidergott ◽  
Haralambie Leahu

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