SMALL TIME BOUNDARY ESTIMATES FOR SOLUTIONS OF THE HEAT-EQUATION WITHNON-COMPATIBLE DATA

lit this Note, we prove small time estimates near the boundary for sol utions of the linens hear equation: u(t) = Delta u in (0, infinity) x Omega, u = 0 on partial derivative Omega, u(0) = phi in Omega, with no n-compatible initial data phi is an element of C(<(Omega)over bar>), w here Omega is a bounded domain of R-N. The proofs nse primarily based on the maximum principle, via the construction of suitable sub- and su per-solutions, and on a monotonicity: argument. We obtain similar resu lts for the associated inhomogeneous problem. A generalization to a la rge class of linear parabolic equations is announced. (C) Academie des Sciences/Elsevier, Paris.