A regularity result for a convex functional  and bounds for the singular
set

Bruno De Maria

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Partial continuity for elliptic problems

Mikil Foss, Giuseppe Mingione (2008)

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We prove some optimal regularity results for minimizers of the integral functional $\int f (x, u, D u) d x$ belonging to the class $K : = {u \in W^{1, p} (Ω) u \geq ψ}$ , where $ψ$ is a fixed function, under standard growth conditions of $p$ -type, i.e. $L^{- 1} {| z |}^{p} \leq f (x, s, z) \leq {L (1 + | z |}^{p}) .$

Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo, Anna Paola Migliorini (2003)

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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 $F (u) = \int_{Ω} a (x) {[h (| D u |)]}^{p (x)} d x$ with $h$ a convex function with general growth (also exponential behaviour is allowed).

Regularity of minimizers for nonconvex vectorial integrals with $p - q$ growth via relaxation methods.

Benedetti, Irene, Mascolo, Elvira (2004)

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Regularity for degenerate elliptic problems via p-harmonic approximation

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Displaying similar documents to “A regularity result for a convex functional and bounds for the singular set”

Partial continuity for elliptic problems

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Regularity for degenerate elliptic problems via p-harmonic approximation

Regularity of minimizers for nonconvex vectorial integrals with $p - q$ growth via relaxation methods.