Displaying similar documents to “Integral representation and Γ -convergence of variational integrals with p ( x ) -growth”

Integrability for vector-valued minimizers of some variational integrals

Francesco Leonetti, Francesco Siepe (2001)

Commentationes Mathematicae Universitatis Carolinae

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We prove that the higher integrability of the data f , f 0 improves on the integrability of minimizers u of functionals ℱ , whose model is ∫ Ω | D u | p + ( det ( D u ) ) 2 - 〈 f , D u 〉 + 〈 f 0 , u 〉 d x , where u : Ω ⊂ ℝ n → ℝ n and p ≥ 2 .

Optimal partial regularity of minimizers of quasiconvex variational integrals

Christoph Hamburger (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove partial regularity with optimal Hölder exponent of vector-valued minimizers of the quasiconvex variational integral ∫ F ( x , u , D u ) d x under polynomial growth. We employ the indirect method of the bilinear form.

A global differentiability result for solutions of nonlinear elliptic problems with controlled growths

Luisa Fattorusso (2008)

Czechoslovak Mathematical Journal

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Let Ω be a bounded open subset of ℝ n , n > 2 . In Ω we deduce the global differentiability result u ∈ H 2 ( Ω , ℝ N ) for the solutions u ∈ H 1 ( Ω , ℝ n ) of the Dirichlet problem u - g ∈ H 0 1 ( Ω , ℝ N ) , - ∑ i D i a i ( x , u , D u ) = B 0 ( x , u , D u ) with controlled growth and nonlinearity q = 2 . The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.