Uniform bounds of minimizers of non-smooth constrained functionals on maps spaces
| Autor: | Marcos Montenegro, Jurandir Ceccon |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Advances in Calculus of Variations. 9:127-141 |
| ISSN: | 1864-8266 1864-8258 |
| DOI: | 10.1515/acv-2014-0019 |
| Popis: | We consider the functional Φ(u) = ∫Ω |∇u|2 d x - ∫Ω G(u)d x constrained to the set EF = {u ∈ W 0 1,2(Ω,ℝ k ) : ∫Ω F(u)d x = 1}, where Ω is a bounded open subset of ℝ n and F,G : ℝ k → ℝ are continuous functions satisfying certain homogeneity conditions. We investigate the L ∞ regularity of minimizers of Φ in EF . Moreover, we establish uniform L ∞ bounds for such minimizers as well as concentration results on Ω̅. In the latter case, we prove that, up to dilations and translations, minimizers behave in a certain sense like a special type of vector bubble. The central difficulty in this study is the fact that the minimizers of Φ do not have an Euler–Lagrange equation associated. |
| Databáze: | OpenAIRE |
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