In a bounded, smooth domain in R^2, we consider a functional I(u) in the supercritical Trudinger–Moser regime. We prove the existence of 1-peak critical points of I (u) for any bounded domain, of 2-peak critical points for non-simply connected domains, and of k-peak critical points if the domain is an annulus.
Beyond the Trudinger-Moser supremum / M. del Pino, M. Musso, B. Ruf. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 44:3-4(2012), pp. 543-576. [10.1007/s00526-011-0444-5]
Beyond the Trudinger-Moser supremum
B. RufUltimo
2012
Abstract
In a bounded, smooth domain in R^2, we consider a functional I(u) in the supercritical Trudinger–Moser regime. We prove the existence of 1-peak critical points of I (u) for any bounded domain, of 2-peak critical points for non-simply connected domains, and of k-peak critical points if the domain is an annulus.
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