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Volume 37 - Issue 4 - 01 December 1994

Contents

Page 2 of 2

Research Article

  • Every Countable Regular Space Without Isolated Points is Connectifiable

  • V. Tzannes
  • Published online by Cambridge University Press:
    20 November 2018, pp. 556-559
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  • It is proved that every countable regular space without isolated points can be embedded densely in a connected Hausdorff space with a dispersion point.

  • Gradient Estimates on Rd

  • Feng-Yu Wang
  • Published online by Cambridge University Press:
    20 November 2018, pp. 560-570
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  • This paper uses both the maximum principle and coupling method to study gradient estimates of positive solutions to Lu = 0 on Rd, where

    with (aij) uniformly positive definite and aij,bi € C1(Rd). We obtain some upper bounds of |∇u|/u and ∥∇u∥∞/∥u∥∞, which imply a Harnack inequality and improve the corresponding results proved in Cranston [4]. Besides, two examples show that our estimates can be sharp.

Page 2 of 2