General boundary value problems for -parabolic equations in a multidimensional cone are considered. Theorems on solvability and smoothness of solutions are proved. Infinite asymptotic expansions of solutions are obtained in a neighbourhood of the conic vertex. The representations for the coefficients of these expansions are also obtained. At last formal asymptotics of the Green function and the Poisson kernels are obtained.
Cite this article
Vladimir Kozlov, Asymptotics of the Green function and Poisson kernels of a mixed parabolic problem in a cone. I.. Z. Anal. Anwend. 8 (1989), no. 2, pp. 131–151DOI 10.4171/ZAA/343