Global higher integrability for parabolic quasiminimizers in metric measure spaces

2015 ◽  
Vol 126 (1) ◽  
pp. 307-339 ◽  
Author(s):  
Mathias Masson ◽  
Mikko Parviainen
Keyword(s):  
Metric Measure Spaces ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Measure Spaces

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 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 Higher Integrability of Weak Solutions to a Class of Double Obstacle Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhenhua Hu ◽  
Shuqing Zhou
Keyword(s):  
Differential Equation ◽  
Weak Solutions ◽  
Second Order ◽  
Obstacle Problems ◽  
Elliptic Differential Equation ◽  
Higher Integrability ◽  
Global Higher Integrability ◽  
Quasilinear Elliptic

We first introduce double obstacle systems associated with the second-order quasilinear elliptic differential equationdiv(A(x,∇u))=div f(x,u), whereA(x,∇u),f(x,u)are twon×Nmatrices satisfying certain conditions presented in the context, then investigate the local and global higher integrability of weak solutions to the double obstacle systems, and finally generalize the results of the double obstacle problems to the double obstacle systems.

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 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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