The boundary behavior and uniqueness of solutions of the heat equation.
F. W. Gehring · Transactions of the American Mathematical Society · 1960
it is not difficult to show that, for each c>0, there exists a constant G = Ci(a) < oo such that /°° C °° Ci | ykyix -y,t)\dyS Cu J I y*™(* -y,l)\dySfor all (x, t)EPia, 0).For functions in 774 we have the following "localization" theorem.Lemma 1. Suppose that wG77A in 0 0.Then, for each xo,as ix, t)-*ixo, 0), OO, and f kix-y,t)daiy)=o(--\(2.3) J,"-, ' '