On the weighted rearrangement of functions and degenerate nonlinear elliptic equations On the weighted rearrangement of functions and degenerate nonlinear elliptic equations

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Abstract

Let Ω be a bounded domain of R<sup>n</sup>. We shall deal with boundary value problems of the following form −∑<sub>i=1</sub><sup>n</sup> ∂ ∕ ∂x<sub>i </sub>(|x|<sup>α</sup> a<sub>i</sub>(x, u, ∇u)) = |x|<sup>α</sup> H(x, u) in Ω, u = g on ∂Ω. Here α > 1 - n, u is the relevant solution, ∇u is its gradient and H is a given real-valued function. Under proper assumptions a pri-ori estimates of solutions u to the problem (0.1) are established by virtue of weighted rearrangement of functions and weighted isoperimetric inequalities.

Journal

  • Mathematical Journal of Ibaraki University

    Mathematical Journal of Ibaraki University 44(0), 17-31, 2012

    College of Science, Ibaraki University

Codes

  • NII Article ID (NAID)
    130003373916
  • NII NACSIS-CAT ID (NCID)
    AA11169155
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    1343-3636
  • Data Source
    IR  J-STAGE 
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