Sharp estimates for semi-stable radial solutions of semilinear elliptic equations

Details Sharp estimates for semi-stable radial solutions of semilinear elliptic equations Sharp estimates for semi-stable radial solutions of semilinear elliptic equations

2009-06-08

arxiv.org/abs/0906.1443v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

This paper is devoted to the study of semi-stable radial solutions $u\in H^1(B_1)$ of $-\Delta u=g(u) {in} B_1\setminus \{0\}$, where $g\in C^1(R)$ is a general nonlinearity and $B_1$ is the unit ball of $R^N$. We establish sharp pointwise estimates for such solutions. As an application of these results, we obtain optimal pointwise estimates for the extremal solution and its derivatives (up to order three) of the semilinear elliptic equation $-\Delta u=\lambda f(u)$, posed in $B_1$, with Dirichlet data $u|_{\partial B_1}=0$, and a continuous, positive, nondecreasing and convex function $f$ on $[0,\infty)$ such that $f(s)/s\to\infty$ as $s\to\infty$.

Affiliated with

Also associated with

No associations

Rating

Sharp estimates for semi-stable radial solutions of semilinear elliptic equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sharp estimates for semi-stable radial solutions of semilinear elliptic equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharp estimates for semi-stable radial solutions of semilinear elliptic equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-231793