Stable minimizers of functionals of the gradient

Mikhail A. Sychev, Giulia Treu, Giovanni Colombo

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

Let Ω ⊂ ℝn be a bounded Lipschitz domain. Let be a continuous function with superlinear growth at infinity, and consider the functional, u ϵ W1,1(Ω). We provide necessary and sufficient conditions on L under which, for all f ϵ W1,1(Ω) such that I(f) < +∞, the problem of minimizing with the boundary condition u|∂Ω = f has a solution which is stable, or - alternatively - is such that all of its solutions are stable. By stability of at u we mean that weakly in W1,1(Ω) together with imply uk → u strongly in W1,1(Ω). This extends to general boundary data some results obtained by Cellina and Cellina and Zagatti. Furthermore, with respect to the preceding literature on existence results for scalar variational problems, we drop the assumption that the relaxed functional admits a continuous minimizer.

Язык оригиналаанглийский
Страницы (с-по)2642-2655
Число страниц14
ЖурналProceedings of the Royal Society of Edinburgh Section A: Mathematics
Том150
Номер выпуска5
DOI
СостояниеОпубликовано - 1 окт 2020

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