Uniform bounds of minimizers of non-smooth constrained functionals on maps spaces

作者：Ceccon Jurandir^*; Montenegro Marcos^*

来源：Advances in Calculus of Variations, 2016, 9(2): 127-141.

DOI：10.1515/acv-2014-0019

• Non-smooth minimization
• regularity
• uniform bounds
• blow-up theory

We consider the functional
Phi(u) = X integral vertical bar del u vertical bar(2) dx - integral G(u) dx
constrained to the set
E-F = {u is an element of W-0(1,2)(Omega, R-k) : integral(Omega) F(u) dx = 1},
where Omega 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-infinity regularity of minimizers of Phi in E-F. Moreover, we establish uniform L-infinity bounds for such minimizers as well as concentration results on (Omega) over bar. 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 Phi do not have an Euler-Lagrange equation associated.

• 出版日期2016-4