Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-10-31T16:28:29.922Z Has data issue: false hasContentIssue false

Essential self-adjointness and self-adjointness for even order elliptic operators

Published online by Cambridge University Press:  14 November 2011

Nguyen Xuan Dung
Affiliation:
Texas Tech University, Lubbock, Texas, U.S.A.

Synopsis

We consider elliptic operators of the form , on L2(Rn), and establish conditions under which T is essentially self-adjoint on , and self-adjoint on H2m(Rn)∩D(q).

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1982

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Agmon, Shmuel. Lectures on Elliptic Boundary Value Problems (New York: D. Van Nostrand, 1965).Google Scholar
2Browder, Felix. Fuctional analysis and partial differential equations. II. Math. Ann. 145 (1962), 81226.Google Scholar
3Brucensev, A. G. and Rofe-Beketov, F. S.. Self-adjointness for higher order elliptic integrals. Functional Anal. Appl. 7 (1973), 319321.CrossRefGoogle Scholar
4Brucensev, A. G. and Rofe-Beketov, F. S.. Self-adjointness conditions for strongly elliptic systems of arbitrary order. Math. USSR-Sb. 24 (1974), 103126.Google Scholar
5Paul, R. Chernoff. Essential self-adjointness of powers of generators of hyperbolic equations. J. Functional Analysis, 12 (1973), 401414.Google Scholar
6Cordes, H. O.. Self-adjointness of powers of elliptic operators on non-compact manifolds. Math. Ann. 195 (1972), 257272.Google Scholar
7Cordes, H. O.. A Global Parametrix for ψdo over Rn, with Applications. Preprint No. 90, Sonderforschungsbereich 72, Universität Bonn, 1976.Google Scholar
8Devinatz, A.. Essential self-adjointness of powers of Schrödinger-type operators. J. Functional Analysis 25 (1977), 5869.CrossRefGoogle Scholar
9Eastham, M. S. P., Evans, W. D. and McLeod, J. B.. The essential self-adjointness of Schrödinger-type operators. Arch. Rational Mech. Anal. 60 (1976), 185204.Google Scholar
10Evans, W. D.. On the essential self-adjointness of powers of Schrödinger-type operators. Proc. Roy. Soc. Edinburgh Sect. A 79 (1977), 151162.Google Scholar
11Everitt, W. N. and Giertz, M.. Inequalities and separtaion for Schrodinger-type operators. Proc. Roy. Soc. Edinburgh Sect. A 79 (1978), 257265.Google Scholar
12Keller, R. G.. The essential self-adjointness of differential operators. Proc. Roy. Soc. Edinburgh Sect. A 82 (1979), 305344.Google Scholar
13Knowles, Ian. Note on a limit-point criterion. Proc. Amer. Math. Soc. 41 (1973), 117119.CrossRefGoogle Scholar
14Sohr, Hermann. Über die Selbstadjungiertheit von Schrödinger-Operatoren. Math. Z. 160 (1978), 255281.Google Scholar
15Subin, M. A.. Pseudodifferential operators in Rn. Soviet Math. Dokl. 12 (1971, 147151. (Added 24 May, 1982)Google Scholar
16Atkinson, F. V.. On some results of Everitt and Giertz. Proc. Roy. Soc. Edinburgh Sect. A 71 (1973), 151158.Google Scholar
17Evans, W. D. and Zettl, A.. Dirichlet and separation results for Schrödinger-type operators. Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), 151162.Google Scholar
18Naimark, M. A.. Linear Differential Operators, Part II (New York: F. Ungar, 1968).Google Scholar