Let be a bounded domain of class in and let be a compact subset of . Assume that and denote by the maximal solution of in which vanishes on . We obtain sharp upper and lower estimates for in terms of the Bessel capacity and prove that is -moderate. In addition we describe the precise asymptotic behavior of at points , which depends on the 'density' of at , measured in terms of the capacity .
Cite this article
Moshe Marcus, Laurent Véron, Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion. J. Eur. Math. Soc. 6 (2004), no. 4, pp. 483–527DOI 10.4171/JEMS/18