0000000000860105
AUTHOR
Marcos Solera
Evolution problems of Leray-Lions type with nonhomogeneous Neumann boundary conditions in metric random walk spaces
Abstract In this paper we study evolution problems of Leray–Lions type with nonhomogeneous Neumann boundary conditions in the framework of metric random walk spaces. This covers cases with the p -Laplacian operator in weighted discrete graphs and nonlocal operators with nonsingular kernel in R N .
$(BV,L^p)$-decomposition, $p=1,2$, of Functions in Metric Random Walk Spaces
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.