Logarithmic Sobolev inequalities for some nonlinear PDE’s. (English) Zbl 1059.60084

Summary: The aim of this paper is to study the behavior of solutions of some nonlinear partial differential equations of MacKean-Vlasov type. The main tools used are, on one hand, the logarithmic Sobolev inequality and its connections with the concentration of measure and the transportation inequality with quadratic cost; on the other hand, the propagation of chaos for particle systems in mean field interaction.


60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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