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Proceedings of the American Mathematical Society

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Relation between growth and regularity of solutions of hypoelliptic equations


Authors: M. Shafii-Mousavi and Z. Zielezny
Journal: Proc. Amer. Math. Soc. 104 (1988), 1103-1110
MSC: Primary 35H05; Secondary 35B05
DOI: https://doi.org/10.1090/S0002-9939-1988-0929423-3
MathSciNet review: 929423
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Abstract: For a class of linear partial differential equations with variable coefficients, it is shown that the Gevrey regularity of solutions depends on their growth at infinity.


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

  • [1] I. M. Gel′fand and G. E. Shilov, Generalized functions. Vol. 2. Spaces of fundamental and generalized functions, Translated from the Russian by Morris D. Friedman, Amiel Feinstein and Christian P. Peltzer, Academic Press, New York-London, 1968. MR 0230128
  • [2] V. V. Grušin, The connection between local and global properties of the solutions of hypo-elliptic equations with constant coefficients, Mat. Sb. (N.S.) 66 (108) (1966), 525–550 (Russian). MR 0178249
  • [3] Lars Hörmander, Linear partial differential operators, Springer Verlag, Berlin-New York, 1976. MR 0404822
  • [4] François Trèves, Linear partial differential equations with constant coefficients: Existence, approximation and regularity of solutions, Mathematics and its Applications, Vol. 6, Gordon and Breach Science Publishers, New York-London-Paris, 1966. MR 0224958

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0929423-3
Article copyright: © Copyright 1988 American Mathematical Society