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Least gradient functions in metric random walk spaces

José M. MazónWojciech Górny

subject

Pure mathematicsControl and Optimization05C81 35R02 26A45 05C21 45C99010102 general mathematicsPoincaré inequalityRandom walk01 natural sciences010101 applied mathematicsComputational Mathematicssymbols.namesakeMathematics - Analysis of PDEsControl and Systems EngineeringMetric (mathematics)FOS: Mathematicssymbols0101 mathematicsAnalysis of PDEs (math.AP)Mathematics

description

In this paper we study least gradient functions in metric random walk spaces, which include as particular cases the least gradient functions on locally finite weighted connected graphs and nonlocal least gradient functions on $\mathbb{R}^N$. Assuming that a Poincar\'e inequality is satisfied, we study the Euler-Lagrange equation associated with the least gradient problem. We also prove the Poincar\'e inequality in a few settings.

yearjournalcountryeditionlanguage
2019-12-29ESAIM: Control, Optimisation and Calculus of Variations
https://doi.org/10.1051/cocv/2020087