Uniqueness theorems for parabolic equations and Martin boundaries for elliptic equations in skew product form

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Author(s)

Abstract

We give a method to determine Martin boundaries of product domains for elliptic equations in skew product form via Widder type uniqueness theorems for parabolic equations. It is shown that the fiber of the Martin boundary at infinity of the base space degenerates into one point if any nonnegative solution to the Dirichlet problem for a corresponding parabolic equation with zero initial and boundary data is identically zero. We apply it in a unified way to several concrete examples to explicitly determine Martin boundaries for them.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 57(2), 387-413, 2005-04-01

    The Mathematical Society of Japan

References:  81

Codes

  • NII Article ID (NAID)
    10016419921
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    7304265
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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