Properties of superharmonic functions satisfying nonlinear inequalities in nonsmooth domains

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Author(s)

Abstract

In a uniform domain Ω, we present a certain reverse mean value inequality and a Harnack type inequality for positive superharmonic functions satisfying a nonlinear inequality -Δ<i>u</i>(<i>x</i>) ≤ <i>c</i>δ<sub>Ω</sub>(<i>x</i>)<sup>-α</sup><i>u</i>(<i>x</i>)<sup><i>p</i></sup> for <i>x</i> ∈ Ω, where <i>c</i> > 0, α ≥ 0 and <i>p</i> > 1 and δ<sub>Ω</sub>(<i>x</i>) is the distance from a point <i>x</i> to the boundary of Ω. These are established by refining a boundary growth estimate obtained in our previous paper (2008). Also, we apply them to show the existence of nontangential limits of quotients of such functions and to give an extension of a certain minimum principle studied by Dahlberg (1976).

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 62(4), 1043-1068, 2010-10-01

    The Mathematical Society of Japan

References:  15

Codes

  • NII Article ID (NAID)
    10027870995
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    10858991
  • 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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