ABSTRACT
The method suggested by Perron for solving the first boundary value problem for the Laplace equation can be applied, with almost no modification, to the first boundary value problem for the heat equation. This chapter gives few lemmas which allow to apply Perron’s method under more general assumptions than those of Sternberg. Just as Perron had proved that his “condition B” is sufficient for the existence of a solution for the Dirichlet problem, the chapter shows that a sufficient condition of regularity of a point P is the existence of a function u¯(x,t) (called “regularity barrier” in the sequel).
