The periodic unfolding method in perforated domains.
Cioranescu, Doina, Donato, Patrizia, Zaki, Rachad (2006)
Portugaliae Mathematica. Nova Série
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Cioranescu, Doina, Donato, Patrizia, Zaki, Rachad (2006)
Portugaliae Mathematica. Nova Série
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Jaeyoung Byeon, Zhi-Qiang Wang (2009)
Annales de l'I.H.P. Analyse non linéaire
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Souto, Marco A. S. (2002)
Abstract and Applied Analysis
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P. H. Rabinowitz, E. Stredulinsky (2004)
Annales de l'I.H.P. Analyse non linéaire
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Luisa Fattorusso (2008)
Czechoslovak Mathematical Journal
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Let be a bounded open subset of , . In we deduce the global differentiability result for the solutions of the Dirichlet problem with controlled growth and nonlinearity . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
Matteo Novaga, Enrico Valdinoci (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider a mesoscopic model for phase transitions in a periodic medium and we construct multibump solutions. The rational perturbative case is dealt with by explicit asymptotics.
Louis Jeanjean, Kazunaga Tanaka (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on . The main difficulties to overcome are the lack of a priori bounds for Palais–Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be...