Displaying similar documents to “On ℒ l o c 2 , n -regularity for the gradient of a weak solution to nonlinear elliptic systems”

On Hölder regularity for vector-valued minimizers of quasilinear functionals

Josef Daněček, Eugen Viszus (2010)

Mathematica Bohemica

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We discuss the interior Hölder everywhere regularity for minimizers of quasilinear functionals of the type 𝒜 ( u ; Ω ) = ∫ Ω A i j α β ( x , u ) D α u i D β u j d x whose gradients belong to the Morrey space L 2 , n - 2 ( Ω , ℝ n N ) .

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.