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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.

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

  • [1] Hector O. Fattorini, The Cauchy problem, Encyclopedia of Mathematics and its Applications, vol. 18, Addison-Wesley Publishing Co., Reading, Mass., 1983. With a foreword by Felix E. Browder. MR 692768
  • [2] Jerome A. Goldstein, Semigroups of linear operators and applications, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1985. MR 790497
  • [3] David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR 737190
  • [4] Rainer Hempel and Jürgen Voigt, On the 𝐿_{𝑝}-spectrum of Schrödinger operators, J. Math. Anal. Appl. 121 (1987), no. 1, 138–159. MR 869525,
  • [5] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • [6] Dan Pascali and Silviu Sburlan, Nonlinear mappings of monotone type, Martinus Nijhoff Publishers, The Hague; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1978. MR 531036
  • [7] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486
  • [8] Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory., Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961
  • [9] H. O. Fattorini, On the angle of dissipativity of ordinary and partial differential operators, Functional analysis, holomorphy and approximation theory, II (Rio de Janeiro, 1981) North-Holland Math. Stud., vol. 86, North-Holland, Amsterdam, 1984, pp. 85–111. MR 771324,
  • [10] Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244

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Keywords: Second order elliptic operators, uniform and degenerate ellipticity, sectorial operators, analytic contraction semigroups
Article copyright: © Copyright 1991 American Mathematical Society