Abstract
where C(xo) = {(x, y): Ix-xol < ~y, o < y < h}, is finite for almost every x o eE. An analogous theorem for solution of the initial-value p rob lem for the heat equat ion has been proved by Ha t t emer [3]. I t is our purpose here to show that a similar theorem also holds for solution of a boundary-va lue p rob lem for the heat equation. I f we hold the t ime variable t fixed, then our result yields Stein's theorem. Because of the geomet ry of the region considered here, we lack a regular izat ion theorem which is used in bo th Stein's and Ha t t emer ' s proofs ; thus a slightly different a rgument is needed, and this a rgument is provided by a certain fo rm of Green ' s Theorem ( L e m m a 1). We use the following nota t ions and conventions:
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
