About this Mathematics article
New solutions for Trudinger–Moser critical equations in R2 by Manuel del Pino; Monica Musso; Bernhard Ruf is a Mathematics article available to read on EtoBox.
Let Ω be a bounded, smooth domain in R 2 . We consider critical points of the Trudinger-Moser type functional in H 1 0 (Ω), namely solutions of the boundary value problem u + λue u 2 = 0 with homogeneous Dirichlet boundary conditions, where λ > 0 is a small parameter. Given k 1 we find conditions under which there exists a solution u λ which blows up at exactly k points in Ω as λ → 0 and J λ (u λ ) → 2kπ. We find that at least one such solution always exists if k = 2 and Ω is not simply connected. If Ω has d 1 holes, in addition d + 1 bubbling solutions with k = 1 exist. These results are existence counterparts of one by Druet in [O. Druet, Multibump analysis in dimension 2: Quantification of blow-up levels, Duke Math. J. 132 (2) (2006) 217-269] which classifies asymptotic bounded energy levels of blow-up solutions for a class of nonlinearities of critical exponential growth, including this one as a prototype case.
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Manuel del Pino; Monica Musso; Bernhard Ruf
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)
- Published
- 2010
- Language
- EN
- Field
- Mathematics (Physical Sciences)