The total variation flow in metric random walkspaces

Fecha: Miércoles 7 de abril de 2021 - 15:00

Lugar: Online - Instrucciones: https://sites.google.com/view/analysis-pde-seminar/

Resumen: Our aim is to study the Total Variation Flow (TVF) in metric random walkspaces (MRWS) which include as particular cases: the TVF on locally finite weighted connected graphs. We introduce the concepts of perimeter and meancurvature for subsets of a MRWS. After proving the existence and uniquenessof solutions of the TVF, we study the asymptotic behaviour of those solutions,and for such aim we establish some inequalities of Poincar ́e type. Furthermore,we introduce the concepts of Cheeger and calibrable sets in metric randomwalk spaces and characterize calibrability by using the 1-Laplacian operator.In connection with the Cheeger cut problem we study the eigenvalue problemwhereby we give a method to solve the optimal Cheeger cut problem.