Pictures below are from Entropy and heat kernel bounds on a Ricci flow background. I don't know what is the mean of barrier sense or viscosity sense. At beginning, I guess they should be the concepts of real analysis. But in the indexes of Rudin's Real and Complex analysis, I can't find them.
In Evans' Partial Differential Equations, there are barrier and viscosity solution. But seemly, they are not connection with the barrier sense or viscosity sense.
If this problem is fussy, telling me to read what book or paper is enough. Thanks.
