Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces

2007 ◽  
Vol 339 (1) ◽  
pp. 101-134 ◽  
Author(s):  
Ilkka Holopainen ◽  
Urs Lang ◽  
Aleksi Vähäkangas
Keyword(s):  
Dirichlet Problem ◽  
Hyperbolic Metric ◽  
Metric Measure Spaces ◽  
Gromov Hyperbolic ◽  
Measure Spaces ◽  
Dirichlet Problem At Infinity

scholarly journals Notions of Dirichlet problem for functions of least gradient in metric measure spaces

2019 ◽  
Vol 35 (6) ◽  
pp. 1603-1648 ◽  
Author(s):  
Riikka Korte ◽  
Panu Lahti ◽  
Xining Li ◽  
Nageswari Shanmugalingam
Keyword(s):  
Dirichlet Problem ◽  
Metric Measure Spaces ◽  
Measure Spaces

scholarly journals Domains in Metric Measure Spaces with Boundary of Positive Mean Curvature, and the Dirichlet Problem for Functions of Least Gradient

2018 ◽  
Vol 29 (4) ◽  
pp. 3176-3220
Author(s):  
Panu Lahti ◽  
Lukáš Malý ◽  
Nageswari Shanmugalingam ◽  
Gareth Speight
Keyword(s):  
Dirichlet Problem ◽  
Mean Curvature ◽  
Metric Measure Spaces ◽  
Measure Spaces

scholarly journals Stability and Continuity of Functions of Least Gradient

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
H. Hakkarainen ◽  
R. Korte ◽  
P. Lahti ◽  
N. Shanmugalingam
Keyword(s):  
Dirichlet Problem ◽  
Maximum Principle ◽  
Measure Zero ◽  
Metric Measure Spaces ◽  
Local Minimizers ◽  
Stability Properties ◽  
Area Functional ◽  
Measure Spaces

Abstract In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.

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
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