The initial-boundary value problems for the heat operator in non-cylindrical domains (Q1389872)

This paper deals with first and second initial-boundary value problems of the heat equation in a bounded domain lying in \(\mathbb{R}^{n+1}\) with \(L^p\) boundary data. The author defines certain mixed (thermal) potentials in terms of the fundamental solution for the heat equation. A number of rather technical assumptions are made, and the analysis is quite delicate, but in the end, the author is able to show that the solutions so obtained assume the proper boundary values.