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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Sectorialness of second order elliptic operators in divergence form

Author: Noboru Okazawa
Journal: Proc. Amer. Math. Soc. 113 (1991), 701-706
MSC: Primary 35J15; Secondary 47D06, 47F05
MathSciNet review: 1072347
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Abstract: A sectorial estimate is given to second order linear elliptic differential operators of divergence form. The estimate is a slight improvement of Pazy's. The obtained constant depends on $ p$ of the space $ {L^p}(\Omega )(1 < p < \infty )$ and does not depend on the operators themselves. The same constant has appeared in the sectorial estimate for second order linear ordinary differential operators due to Fattorini.

The result is in connection with Stein's estimate of the analytic semigroups generated by linear elliptic differential operators.

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Additional Information

PII: S 0002-9939(1991)1072347-4
Keywords: Second order elliptic operators, uniform and degenerate ellipticity, sectorial operators, analytic contraction semigroups
Article copyright: © Copyright 1991 American Mathematical Society