Linear Partial Differential Operators

contained in D. Weshall use this identifi.cation throughout and thus for an arbitrary set ACR,. write c:(A) = {tp; IJlEC~(R,.), supptpCA}. 1 This means that the tepelegy in .9' is strenger than that induced there by Efl~>,k and that the tepelegy in Efl~>,k is strenger than the ene induced by .9''. Hence the necessity also follows from Theorem 2.2.2. n means that Go, A (0, e, e) > 0 if p m (0, e) = 0 and 1: p~l (0, e) N; = 0, 1 e ER .. , Iei = 1. Since the coefficient of A in (8.4.12) is 4 (.f p (o, e)N;r Front Matter....Pages N2-VII Distribution theory....Pages 1-33 Some special spaces of distributions....Pages 33-62 Existence and approximation of solutions of differential equations....Pages 63-96 Interior regularity of solutions of differential equations....Pages 96-114 The Cauchy problem (constant coefficients)....Pages 114-155 Differential equations which have no solutions....Pages 156-170 Differential operators of constant strength....Pages 170-180 Differential operators with simple characteristics....Pages 180-230 The Cauchy problem (variable coefficients)....Pages 230-241 Elliptic boundary problems....Pages 242-274 Back Matter....Pages 275-287