In this seminar, we will discuss how Neumann-type conditions can be defined for nonlocal equations. In analogy with the local case, these conditions arise from an integration-by-parts formula introduced by Dipierro, Ros-Oton and Valdinoci. We will explain the main differences between these conditions and classical Neumann conditions. Finally, we will see that they provide a suitable framework for modelling a nonlocal chemotaxis problem and that, to obtain uniform estimates, the study of this problem can be reduced to that of a Lane--Emden equation in a half-space. 

Based on joint work with Eleonora Cinti (UNIBO) and Tobias Weth (GUF).