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Transactions of the American Mathematical Society

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Generalized super-solutions of parabolic equations

Author: Neil A. Eklund
Journal: Trans. Amer. Math. Soc. 220 (1976), 235-242
MSC: Primary 35K10
Erratum: Trans. Amer. Math. Soc. 247 (1979), 317-318.
MathSciNet review: 0473522
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Abstract: Let L be a linear, second order parabolic operator in divergence form and let Q be a bounded cylindrical domain in $ {E^{n + 1}}$. Super-solutions of $ Lu = 0$ are defined and generalized to three equivalent forms. Generalized super-solutions are shown to satisfy a minimum principle and form a lattice.

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

  • [7] Neil A. Eklund, Existence and representation of solutions of parabolic equations, Proc. Amer. Math. Soc. 47 (1975), 137-142. MR 0361442 (50:13887)
  • [8] Neil Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 206-226. MR 37 #1758. MR 0226168 (37:1758)

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Keywords: Parabolic PDE, super-solutions, potential theory
Article copyright: © Copyright 1976 American Mathematical Society

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