Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Pseudo-differential estimates for linear parabolic operators

Author: David Ellis
Journal: Trans. Amer. Math. Soc. 184 (1973), 355-371
MSC: Primary 35K30; Secondary 35S10
MathSciNet review: 0333458
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In recent papers, S. Kaplan and D. Ellis have used singular integral operator theory, multilinear interpolation and forms of the classical ``energy inequality'' to obtain results for linear parabolic operators. For higher order linear parabolic operators the local estimates were globalized by a Gårding type partition of unity. In the present paper it is shown how the theory of pseudo-differential operators can be used to study linear parabolic operators without recourse to multilinear interpolation. We also prove that the Gårding type partition of unity is square summable in the Sobolev type spaces $ {H^S}$ and $ {\mathcal{K}^{r,S}}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35K30, 35S10

Retrieve articles in all journals with MSC: 35K30, 35S10

Additional Information

Keywords: Pseudo-differential operator, evolution operator, Gårding type partition of unity, Sobolev space, energy inequality
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society