The Heat Kernel — Heat Equation on the Boundary

6 Heat Equation on the Boundary

In this section, we study the boundary condition we discovered previously in a bit more detail. Our goal is to understand the regularity properties and obtain some estimates of the kernel. In a sense, the work is not very complete, and the reader might feel we stopped abruptly halfway. We just do the bare minimum required to get through the computations needed in the next section when we glue these with the corresponding results in the interior.