Displaying similar documents to “Some regularity results for minimal crystals”

On a Volume Constrained Variational Problem in SBV²(Ω): Part I

Ana Cristina Barroso, José Matias (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider the problem of minimizing the energy E ( u ) : = ∫ Ω | ∇ u ( x ) | 2 d x + ∫ S u ∩ Ω 1 + | [ u ] ( x ) | d H N - 1 ( x ) among all functions ∈ ²(Ω) for which two level sets { u = l i } have prescribed Lebesgue measure α i . Subject to this volume constraint the existence of minimizers for (.) is proved and the asymptotic behaviour of the solutions is investigated.

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

Sabine Schemm (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider higher order functionals of the form F [ u ] = ∫ Ω f ( D m u ) d x for u : ℝ n ⊃ Ω → ℝ N , where the integrand f : ⨀ m ( ℝ n , ℝ N ) → 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 γ | A | p ≤ f ( A ) ≤ L ( 1 + | A | q ) for all A ∈ ⨀ m ( ℝ n , ℝ N ) , with

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

Sabine Schemm (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider higher order functionals of the form F [ u ] = ∫ Ω f ( D m u ) d x for u : ℝ n ⊃ Ω → ℝ N , where the integrand f : ⨀ m ( ℝ n , ℝ N ) → 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 γ | A | p ≤ f ( A ) ≤ L ( 1 + | A | q ) for all A ∈ ⨀ m ( ℝ n , ℝ N ) , with