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Generalizations of results of Agmon and Nirenberg to the Cauchy problem for evolution equations


Author: Monty J. Strauss
Journal: Proc. Amer. Math. Soc. 35 (1972), 431-435
MSC: Primary 35S10
DOI: https://doi.org/10.1090/S0002-9939-1972-0310479-4
MathSciNet review: 0310479
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Abstract: Uniqueness and norm convexity for evolution equations are investigated by using tools developed by Agmon and Nirenberg.


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

  • [1] S. Agmon, Unicité et convexité dans les problèmes différentiels, Séminaire de Mathématiques Supérieures, no. 13 (Été, 1965), Les Presses de l'Université de Montréal, Montréal, Que., 1966. MR 40 #6025. MR 0252808 (40:6025)
  • [2] S. Agmon and L. Nirenberg, Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math. 16 (1963), 121-239. MR 27 #5142. MR 0155203 (27:5142)
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  • [5] L. Nirenberg, Pseudo-differential operators, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R.I., 1970, pp. 149-167. MR 42 #5108. MR 0270217 (42:5108)
  • [6] M. Strauss, Uniqueness and norm convexity for the Cauchy problem, Thesis, New York University, 1971.
  • [7] -, Uniqueness and norm convexity in the Cauchy problem for evolution equations with convolution operators, Proc. Amer. Math. Soc. 35 (1972), 423-430. MR 0310478 (46:9576)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0310479-4
Keywords: Uniqueness, Cauchy problem, evolution equation, pseudo-differential operator
Article copyright: © Copyright 1972 American Mathematical Society

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