scholarly journals Higher integrability for vector-valued parabolic quasi-minimizers on metric measure spaces

2016 ◽  
Vol 54 (1) ◽  
pp. 85-123 ◽  
Author(s):  
Jens Habermann
Keyword(s):  
Metric Measure Spaces ◽  
Higher Integrability ◽  
Measure Spaces ◽  
Vector Valued

Global higher integrability for non-quadratic parabolic quasi-minimizers on metric measure spaces

2017 ◽  
Vol 10 (3) ◽  
pp. 267-301 ◽  
Author(s):  
Yohei Fujishima ◽  
Jens Habermann
Keyword(s):  
Boundary Data ◽  
Measure Space ◽  
Metric Measure Spaces ◽  
Optimal Conditions ◽  
Open Domain ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Starting Point ◽  
Measure Spaces ◽  
Stability Issues

AbstractWe prove up-to-the-boundary higher integrability estimates for parabolic quasi-minimizers on a domain \Omega_{T}= Ω \times (0,T), where Ω denotes an open domain in a doubling metric measure space which supports a Poincaré inequality. The higher integrability for upper gradients is shown globally and under optimal conditions on the boundary \partialΩ of the domain as well as on the boundary data itself. This is a starting point for a further discussion on parabolic quasi-minima on metric measure spaces, such as for example regularity or stability issues.

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

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
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