TITLE

# Large solutions to the p-Laplacian for large p

AUTHOR(S)
García-Melián, Jorge; Rossi, Julio; Lis, José
PUB. DATE
February 2008
SOURCE
Calculus of Variations & Partial Differential Equations;Feb2008, Vol. 31 Issue 2, p187
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
In this work we consider the behaviour for large values of p of the unique positive weak solution u p to Î” p u = u q in Î©, u = +âˆž on $$\partial\Omega$$ , where q > p âˆ’ 1. We take q = q( p) and analyze the limit of u p as p â†’ âˆž. We find that when q( p)/ p â†’ Q the behaviour strongly depends on Q. If 1 < Q < âˆž then solutions converge uniformly in compacts to a viscosity solution of $${\rm max}\{- \Delta_\infty{u}, -|\nabla u| +u^Q \} = 0$$ with u = +âˆž on $$\partial\Omega$$ . If Q = 1 then solutions go to âˆž in the whole Î© and when Q = âˆž solutions converge to 1 uniformly in compact subsets of Î©, hence the boundary blow-up is lost in the limit.
ACCESSION #
27175308

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