Geodesic
Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion
Journal of the European Mathematical Society, Tome 6 (2004) no. 4, pp. 483-527.

Voir la notice de l'article provenant de la source EMS Press

Let Ω be a bounded domain of class C2 in RN and let K be a compact subset of ∂Ω. Assume that q≥(N+1)/(N−1) and denote by UK​ the maximal solution of −Δu+uq=0 in Ω which vanishes on ∂Ω∖K. We obtain sharp upper and lower estimates for UK​ in terms of the Bessel capacity C2/q,q′​ and prove that UK​ is σ-moderate. In addition we describe the precise asymptotic behavior of UK​ at points σ∈K, which depends on the “density” of K at σ, measured in terms of the capacity C2/q,q′​.
DOI : 10.4171/jems/18
Classification : 35-XX, 31-XX, 00-XX
Keywords: Bessel capacities, maximal solutions, rate of blow-up 
@article{JEMS_2004_6_4_a4,
     author = {Moshe Marcus and Laurent V\'eron},
     title = {Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion},
     journal = {Journal of the European Mathematical Society},
     pages = {483--527},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2004},
     doi = {10.4171/jems/18},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/18/}
}
TY  - JOUR
AU  - Moshe Marcus
AU  - Laurent Véron
TI  - Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion
JO  - Journal of the European Mathematical Society
PY  - 2004
SP  - 483
EP  - 527
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/18/
DO  - 10.4171/jems/18
ID  - JEMS_2004_6_4_a4
ER  - 
%0 Journal Article
%A Moshe Marcus
%A Laurent Véron
%T Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion
%J Journal of the European Mathematical Society
%D 2004
%P 483-527
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/18/
%R 10.4171/jems/18
%F JEMS_2004_6_4_a4
Moshe Marcus; Laurent Véron. Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion. Journal of the European Mathematical Society, Tome 6 (2004) no. 4, pp. 483-527. doi : 10.4171/jems/18. http://geodesic.mathdoc.fr/articles/10.4171/jems/18/

Cité par Sources :