scholarly journals Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces with the Radon–Nikodym Property

2009 ◽  
Vol 19 (4) ◽  
pp. 1017-1028 ◽  
Author(s):  
Jeff Cheeger ◽  
Bruce Kleiner
Keyword(s):  
Banach Spaces ◽  
Metric Measure Spaces ◽  
Lipschitz Maps ◽  
Measure Spaces ◽  
Nikodym Property

scholarly journals METRIC DIFFERENTIABILITY OF LIPSCHITZ MAPS

2013 ◽  
Vol 96 (1) ◽  
pp. 25-35 ◽  
Author(s):  
DONATELLA BONGIORNO
Keyword(s):  
Banach Spaces ◽  
Lipschitz Mappings ◽  
Lipschitz Maps ◽  
Nikodym Property

AbstractAn extension of Rademacher’s theorem is proved for Lipschitz mappings between Banach spaces without the Radon–Nikodým property.

scholarly journals Density and Extension of Differentiable Functions on Metric Measure Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 254-268
Author(s):  
Rafael Espínola García ◽  
Luis Sánchez González
Keyword(s):  
Banach Spaces ◽  
Metric Measure Spaces ◽  
Differentiable Structure ◽  
First Order ◽  
Differentiable Functions ◽  
Measure Spaces ◽  
The Given ◽  
Vector Valued

Abstract We consider vector valued mappings defined on metric measure spaces with a measurable differentiable structure and study both approximations by nicer mappings and regular extensions of the given mappings when defined on closed subsets. Therefore, we propose a first approach to these problems, largely studied on Euclidean and Banach spaces during the last century, for first order differentiable functions de-fined on these metric measure spaces.

scholarly journals Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces

2017 ◽  
Vol 272 (8) ◽  
pp. 3311-3346 ◽  
Author(s):  
Alexander Grigor'yan ◽  
Eryan Hu ◽  
Jiaxin Hu
Keyword(s):  
Dirichlet Forms ◽  
Heat Kernels ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Non Local

Jump processes and nonlinear fractional heat equations on metric measure spaces

2006 ◽  
Vol 279 (1-2) ◽  
pp. 150-163 ◽  
Author(s):  
Jiaxin Hu ◽  
Martina Zähle
Keyword(s):  
Jump Processes ◽  
Heat Equations ◽  
Metric Measure Spaces ◽  
Measure Spaces

scholarly journals A note on the extension of BV functions in metric measure spaces

2008 ◽  
Vol 340 (1) ◽  
pp. 197-208 ◽  
Author(s):  
Annalisa Baldi ◽  
Francescopaolo Montefalcone
Keyword(s):  
Metric Measure Spaces ◽  
Bv Functions ◽  
Measure Spaces

scholarly journals Well-posedness of Lagrangian flows and continuity equations in metric measure spaces

2014 ◽  
Vol 7 (5) ◽  
pp. 1179-1234 ◽  
Author(s):  
Luigi Ambrosio ◽  
Dario Trevisan
Keyword(s):  
Well Posedness ◽  
Metric Measure Spaces ◽  
Continuity Equations ◽  
Measure Spaces

scholarly journals Discretization of integrals on compact metric measure spaces

2021 ◽  
Vol 381 ◽  
pp. 107602
Author(s):  
Martin D. Buhmann ◽  
Feng Dai ◽  
Yeli Niu
Keyword(s):  
Metric Measure Spaces ◽  
Measure Spaces
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