On the weighted rearrangement of functions and degenerate nonlinear elliptic equations

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概要

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• Let Ω be a bounded domain of Rn. We shall deal with boundary value problems of the following form −∑i=1n ∂ ∕ ∂xi (|x|α ai(x, u, ∇u)) = |x|α 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.

著者

• Ando Hiroshi

  Ibaraki University

• HORIUCHI Toshio

  Ibaraki University

関連論文

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

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