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Displaying similar documents to “Boundary regularity of weak solutions to nonlinear elliptic obstacle problems.”

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.