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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).

Everywhere regularity for vectorial functionals with general growth

Elvira Mascolo, Anna Paola Migliorini (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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).

Existence and regularity of minima for integral functionals noncoercive in the energy space

Lucio Boccardo, Luigi Orsina (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Existence and regularity of minimizers of nonconvex integrals with p-q growth

Pietro Celada, Giovanni Cupini, Marcello Guidorzi (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We show that local minimizers of functionals of the form $\int_{Ω} [f (D u (x)) + g (x, u (x))] d x$ , $u \in u_{0} + W_{0}^{1, p} (Ω)$ , are locally Lipschitz continuous provided f is a convex function with $p - q$ growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.

Existence and regularity of optimal solution for a dead oil isotherm problem.

Sidi Ammi, Moulay Rchid, Torres, Delfim F.M. (2007)

APPS. Applied Sciences

Existence of lipschitzian solutions to the classical problem of the calculus of variations in the autonomous case

A. Cellina, A. Ferriero (2003)

Annales de l'I.H.P. Analyse non linéaire

Existence of regular solutions for a one-dimensional simplified perfect-plastic problem with a unilateral gradient constraint.

Astruc, Thierry (1997)

Journal of Convex Analysis

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