On some methods of the obtaining of a priori pointwise estimates of Dirichlet problem solution for Emden-Fouler equation

Details On some methods of the obtaining of a priori pointwise estimates of Dirichlet problem solution for Emden-Fouler equation On some methods of the obtaining of a priori pointwise estimates of Dirichlet problem solution for Emden-Fouler equation

2003-11-29

arxiv.org/abs/math/0312009v2

Mathematics

Analysis of PDEs

14 pages, Latex 2e

Scientific paper

In this paper we propose some approaches for finding of pointwise estimates of a solution of the Dirichlet boundary value problem $-\Delta u \pm |u|^{q-1} u = 0 $, $|u|=k$ when $|x|=d<1$ and $|u|=0$ when $|x|=1$ where $x\in \Omega = \{x| d<|x|<1\}$. Along with these we consider the same boundary conditions for the Laplace equation and get appropriate estimates for this easier case. We indicate some way what permit to find upper and lower estimates of a solution with explicit constants in turns.

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