Oblique derivative problems
The oblique derivative problem is a boundary value problem for a differential equation that prescribes a directional derivative on the boundary of the domain with the direction never tangential. I have written a book on this topic Oblique Derivative Problems for Elliptic Equations, published by World Scientific in 2013. Here is a link to the publisher's webpage, and here is a link to the errata for this book.
Parabolic differential equations
Parabolic differential equations are partial differential equations modeled on the heat equation. My book on this topic is Second Order Differential Equations, published in 1996 by World Scientific with a second edition published in 2005. Here is a link to the publisher's webpage, and here is a link to the errata for the second edition.