Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1991-1072347-4
MathSciNet review: 1072347
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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

  • [1] H. O. Fattorini, The Cauchy problem, Encyclopedia Math. Appl., vol. 18, Addison-Wesley, Reading, MA, 1983; Cambridge Univ. Press, New York, 1984. MR 692768 (84g:34003)
  • [2] J. A. Goldstein, Semigroups of linear operators and applications, Oxford Univ. Press, New York, 1985. MR 790497 (87c:47056)
  • [3] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Grundlehren Math. Wiss., vol. 224, Springer-Verlag, Berlin and New York, 1977; 2nd ed., 1983. MR 737190 (86c:35035)
  • [4] R. Hempel and J. Voigt, On the $ {L_p}$-spectrum of Schrödinger operators, J. Math. Anal. Appl. 121 (1987), 138-159. MR 869525 (88i:35114)
  • [5] T. Kato, Perturbation theory for linear operators, Grundlehren Math. Wiss., vol. 132, Springer-Verlag, Berlin and New York, 1966; 2nd ed., 1976. MR 0203473 (34:3324)
  • [6] D. Pascali and S. Sburlan, Nonlinear mappings of monotone type, Sijthoff & Noordhoff International Publ., Alphen aan den Rijn, 1978. MR 531036 (80g:47056)
  • [7] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Appl. Math. Sci., vol. 44, Springer-Verlag, New York, 1983. MR 710486 (85g:47061)
  • [8] E. M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory, Ann. of Math. Studies no. 63, Princeton Univ. Press, Princeton, NJ, 1970. MR 0252961 (40:6176)
  • [9] H. O. Fattorini, On the angle of dissipativity of ordinary and partial differential operators, Functional Analysis, Holomorphy and Approximation Theory. II (G. I. Zapata, ed.), Math. Studies, vol. 86, North-Holland, Amsterdam and New York, 1984, pp. 85-111. MR 771324 (86h:47080)
  • [10] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer-Verlag, Berlin and New York, 1981. MR 610244 (83j:35084)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35J15, 47D06, 47F05

Retrieve articles in all journals with MSC: 35J15, 47D06, 47F05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1072347-4
Keywords: Second order elliptic operators, uniform and degenerate ellipticity, sectorial operators, analytic contraction semigroups
Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society