Displaying similar documents to “Integrability for vector-valued minimizers of some variational integrals”

Pointwise estimates of nonnegative subsolutions of quasilinear elliptic equations at irregular boundary points

Jan Malý (1996)

Commentationes Mathematicae Universitatis Carolinae

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Let u be a weak solution of a quasilinear elliptic equation of the growth p with a measure right hand term μ . We estimate u ( z ) at an interior point z of the domain Ω , or an irregular boundary point z ∈ ∂ Ω , in terms of a norm of u , a nonlinear potential of μ and the Wiener integral of 𝐑 n ∖ Ω . This quantifies the result on necessity of the Wiener criterion.

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.

Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo, Anna Paola Migliorini (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove Lipschitz continuity for local minimizers of integral functionals of the Calculus of Variations in the vectorial case, where the energy density depends explicitly on the space variables and has general growth with respect to the gradient. One of the models is F u = ∫ Ω a ( x ) [ h | D u | ] p ( x ) d x with h a convex function with general growth (also exponential behaviour is allowed).

Integral representation and Γ -convergence of variational integrals with p ( x ) -growth

Alessandra Coscia, Domenico Mucci (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the integral representation properties of limits of sequences of integral functionals like ∫ f ( x , D u ) d x under nonstandard growth conditions of ( p , q ) -type: namely, we assume that | z | p ( x ) ≤ f ( x , z ) ≤ L ( 1 + | z | p ( x ) ) . Under weak assumptions on the continuous function p ( x ) , we prove Γ -convergence to integral functionals of the same type. We also analyse the case of integrands f ( x , u , D u ) depending explicitly on u ; finally we weaken the assumption allowing p ( x ) to be discontinuous on nice sets.