scholarly journals Gradient flow for the Boltzmann entropy and Cheeger’s energy on time-dependent metric measure spaces

2017 ◽  
Vol 57 (1) ◽  
Author(s):  
Eva Kopfer
Keyword(s):  
Gradient Flow ◽  
Time Dependent ◽  
Metric Measure Spaces ◽  
Boltzmann Entropy ◽  
Measure Spaces

Heat Flow on Time-Dependent Metric Measure Spaces and Super-Ricci Flows

2018 ◽  
Vol 71 (12) ◽  
pp. 2500-2608 ◽  
Author(s):  
Eva Kopfer ◽  
Karl-Theodor Sturm
Keyword(s):  
Heat Flow ◽  
Time Dependent ◽  
Metric Measure Spaces ◽  
Ricci Flows ◽  
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 The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

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
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