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Proceedings of the American Mathematical Society

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Generalized parabolic functions using the Perron-Wiener-Brelot method

Author: Neil Eklund
Journal: Proc. Amer. Math. Soc. 74 (1979), 247-253
MSC: Primary 35K20
MathSciNet review: 524295
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Abstract: Let L be a linear, second order parabolic operator in divergence form and let U be a bounded domain in $ {E^{n + 1}}$. The Dirichlet problem for $ Lu = 0$ is solved in U using the Perron-Wiener-Brelot method.

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

  • [1] Neil Eklund, Existence and representation of solutions of parabolic equations, Proc. Amer. Math. Soc. 47 (1975), 137-142. MR 0361442 (50:13887)
  • [2] -, Generalized super-solutions of parabolic equations, Trans. Amer. Math. Soc. 220 (1976), 235-242. MR 0473522 (57:13188)
  • [3] -, Convergent nets of parabolic and generalized super-parabolic functions, Proc. Amer. Math. Soc. 50 (1975), 237-243. MR 0509707 (58:23066)

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Keywords: Parabolic PDE, Perron-Wiener-Brelot solution, subsolutions.ams78
Article copyright: © Copyright 1979 American Mathematical Society

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