Search results for " 05C21"

showing 2 items of 2 documents

Least gradient functions in metric random walk spaces

2019

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.

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)MathematicsESAIM: Control, Optimisation and Calculus of Variations
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$(BV,L^p)$-decomposition, $p=1,2$, of Functions in Metric Random Walk Spaces

2019

In this paper we study the $(BV,L^p)$-decomposition, $p=1,2$, of functions in metric random walk spaces, a general workspace that includes weighted graphs and nonlocal models used in image processing. We obtain the Euler-Lagrange equations of the corresponding variational problems and their gradient flows. In the case $p=1$ we also study the associated geometric problem and the thresholding parameters.

Discrete mathematicsApplied MathematicsImage processingWorkspaceRandom walkThresholding05C80 35R02 05C21 45C99 26A45Mathematics - Analysis of PDEsMetric (mathematics)Decomposition (computer science)FOS: MathematicsAnalysisMathematicsAnalysis of PDEs (math.AP)
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