Geodesic
Anomalous large-time behaviour of the $p$-Laplacian flow in an exterior domain in low dimension
Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 249-277.

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We study the large time behaviour of weak nonnegative solutions of the p-Laplace equation posed in an exterior domain in space dimension Nboundary conditions u=0. The description is done in terms of matched asymptotics: the outer asymptotic profile is a dipole-like self-similar solution with a singularity at x=0 and anomalous similarity exponents. The inner asymptotic behaviour is given by a separate-variable profile. We gather both estimates in a global approximant and we also study the behaviour of the free boundary for compactly supported solutions. We complete in this way the analysis made in a previous work for high space dimensions N≥p, a range in which the large-time influence of the holes is less dramatic.
DOI : 10.4171/jems/197
Classification : 35-XX, 00-XX
Keywords: p-Laplacian equation, exterior domain, asymptotic behaviour, domain with holes, matched asymptotics, anomalous self-similarity 
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     author = {Razvan Gabriel Iagar and Juan Luis V\'azquez},
     title = {Anomalous large-time behaviour of the $p${-Laplacian} flow in an exterior domain in low dimension},
     journal = {Journal of the European Mathematical Society},
     pages = {249--277},
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     volume = {12},
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     year = {2010},
     doi = {10.4171/jems/197},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/197/}
}
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Razvan Gabriel Iagar; Juan Luis Vázquez. Anomalous large-time behaviour of the $p$-Laplacian flow in an exterior domain in low dimension. Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 249-277. doi : 10.4171/jems/197. http://geodesic.mathdoc.fr/articles/10.4171/jems/197/

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