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Proceedings of the American Mathematical Society

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A note on complete integrals

Author: Wojciech Chojnacki
Journal: Proc. Amer. Math. Soc. 123 (1995), 393-401
MSC: Primary 35F05; Secondary 58A20
MathSciNet review: 1234624
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Abstract: We present a theorem concerning the representation of solutions of a first-order partial differential equation in terms of a complete integral of the equation. We discuss the geometrical significance of that theorem.

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

    R. Courant and D. Hilbert, Methods of mathematical physics, Vol. 2, Interscience, New York, 1962.
  • Alberto Dou, Lectures on partial differential equations of first order, University of Notre Dame Press, Notre Dame, Ind.-London, 1972. MR 0599577
  • V. V. Lyčagin, Local classification of first order nonlinear partial differential equations, Uspehi Mat. Nauk 30 (1975), no. 1(181), 101–171 (Russian). MR 0420679
  • Ian N. Sneddon, Elements of partial differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1957. MR 0082600

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Keywords: First-order partial differential equation, complete integral, envelope
Article copyright: © Copyright 1995 American Mathematical Society