Fading absorption in non-linear elliptic equations

The purpose of this note is to correct an error that occurred in the proof of Theorem 1.2 of the paper ‘Fading absorption in non-linear elliptic equations’ which appeared in

- We prove here the existence of a positive solution, under general conditions, for semilinear elliptic equations in unbounded domains with a variational structure..

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des

E., Dead cores and instanteous compactification of the support of energy solutions of quasilinear parabolic equations of arbitrary order, Sbornik: Mathematics 190 :12 (1999),

V´ eron, The boundary trace of positive solutions of semilinear elliptic equations: the subcritical case. V´ eron, The boundary trace of positive solutions of semilinear

V´eron, Boundary trace of positive solutions of semilinear elliptic equations in Lipschitz domains: the subcritical case, Ann. V´eron, Boundary trace of positive solutions

and Shishkov A.E., Saint-Venant’s principle in blow-up for higher-order quasilinear parabolic equations, Proc. and V´ eron L., Initial trace of positve solutions to semilinear

In the general case, assuming that Ω possesses a tangent cone at every boundary point and q is subcritical, we prove an existence and uniqueness result for positive solutions