Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Partial regularity of minimizers of higher order integrals with (, )-growth

ESAIM: Control, Optimisation and Calculus of Variations

We consider higher order functionals of the form $F\left[u\right]=\underset{\Omega }{\int }f\left({D}^{m}u\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x\phantom{\rule{2.0em}{0ex}}\text{for}\phantom{\rule{4.0pt}{0ex}}u:{ℝ}^{n}\supset \Omega \to {ℝ}^{N},$ where the integrand $f:{⨀}^{m}\left({ℝ}^{n},{ℝ}^{N}\right)\to ℝ$, m 1 is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the (p, q)-growth condition ${\gamma |A|}^{p}\le f\left(A\right)\le {L\left(1+|A|}^{q}\right)\phantom{\rule{2.0em}{0ex}}\text{for}\phantom{\rule{4.0pt}{0ex}}\text{all}\phantom{\rule{4.0pt}{0ex}}A\in {⨀}^{m}\left({ℝ}^{n},{ℝ}^{N}\right),$ with γ...

Partial regularity of minimizers of higher order integrals with (, )-growth

ESAIM: Control, Optimisation and Calculus of Variations

We consider higher order functionals of the form $F\left[u\right]=\underset{\Omega }{\int }f\left({D}^{m}u\right)\phantom{\rule{0.166667em}{0ex}}\mathrm{d}x\phantom{\rule{2.0em}{0ex}}\text{for}\phantom{\rule{4.0pt}{0ex}}u:{ℝ}^{n}\supset \Omega \to {ℝ}^{N},$ where the integrand $f:{⨀}^{m}\left({ℝ}^{n},{ℝ}^{N}\right)\to ℝ$, m 1 is strictly quasiconvex and satisfies a non-standard growth condition. More precisely we assume that f fulfills the (p, q)-growth condition ${\gamma |A|}^{p}\le f\left(A\right)\le {L\left(1+|A|}^{q}\right)\phantom{\rule{2.0em}{0ex}}\text{for}\phantom{\rule{4.0pt}{0ex}}\text{all}\phantom{\rule{4.0pt}{0ex}}A\in {⨀}^{m}\left({ℝ}^{n},{ℝ}^{N}\right),$ with γ...

Page 1