# A priori estimate for a family of semi-linear elliptic equations with critical nonlinearity - Mathematics > Analysis of PDEs

A priori estimate for a family of semi-linear elliptic equations with critical nonlinearity - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider positive solutions of $\Delta u-\mu u+Ku^{\frac{n+2}{n-2}}=0$ on$B 1$ $n\ge 5$ where $\mu $ and $K>0$ are smooth functions on $B 1$. If $K$is very sub-harmonic at each critical point of $K$ in $B {2-3}$ and the maximumof $u$ in $\bar B {1-3}$ is comparable to its maximum over $\bar B 1$, then allpositive solutions are uniformly bounded on $\bar B {1-3}$. As an application,a priori estimate for solutions of equations defined on $\mathbb S^n$ isderived.

Author: ** Lei Zhang**

Source: https://arxiv.org/