A characterization of Sobolev spaces by solutions of heat equation and a stability problem for a functional equation
Commun. Korean Math. Soc. 2008 Vol. 23, No. 3, 401-411 Printed September 1, 2008
Yun-Sung Chung, Young-Su Lee, Deok-Yong Kwon, and Soon-Yeong Chung Sungkyunkwan University, KAIST, Sogang University, Sogang University
Abstract : In this paper, we characterize Sobolev spaces $\mathcal H^s(\mathbb R^n),~s\in\mathbb R$ by the initial value of solutions of heat equation with a growth condition. By using an idea in its proof, we also discuss a stability problem for Cauchy functional equation in the Sobolev spaces.