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The essential self-adjointness of differential operators with positive coefficients

Published online by Cambridge University Press:  14 November 2011

R. G. Keller
R. G. Keller
Affiliation:
Mathematics Institute, University of Oxford
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Extract

We consider the formally self-adjoint 2mth-order elliptic differential operator in ℝn given by where lt is an operator of order t, and pt ≧0 for t ≧1 and establish conditions under which the operator on is essentially self-adjoint in L2. A feature is that the major conditions (including the positivity of the coefficients) have to be imposed only in an increasing sequence of annular regions surrounding the origin.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 3-4 , 1979 , pp. 345 - 360
Copyright
Copyright © Royal Society of Edinburgh 1979

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References

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