Memoirs of the American Mathematical Society 2012; 105 pp; softcover Volume: 218 ISBN10: 0821869094 ISBN13: 9780821869093 List Price: US$70 Individual Members: US$42 Institutional Members: US$56 Order Code: MEMO/218/1027
 The authors prove some refined asymptotic estimates for positive blowup solutions to \(\Delta u+\epsilon u=n(n2)u^{\frac{n+2}{n2}}\) on \(\Omega\), \(\partial_\nu u=0\) on \(\partial\Omega\), \(\Omega\) being a smooth bounded domain of \(\mathbb{R}^n\), \(n\geq 3\). In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when \(n=3\) or \(n\geq 7\). As a direct consequence, they prove the validity of the LinNi's conjecture in dimension \(n=3\) and \(n\geq 7\) for mean convex domains and with bounded energy. Recent examples by WangWeiYan show that the bound on the energy is a necessary condition. Table of Contents  Introduction
 \(L^\infty\)bounded solutions
 Smooth domains and extensions of solutions to elliptic equations
 Exhaustion of the concentration points
 A first upperestimate
 A sharp upperestimate
 Asymptotic estimates in \(C^1\left(\Omega\right)\)
 Convergence to singular harmonic functions
 Estimates of the interior blowup rates
 Estimates of the boundary blowup rates
 Proof of Theorems 1 and 2
 Appendix A. Construction and estimates on the Green's function
 Appendix B. Projection of the test functions
 Bibliography
