Displaying similar documents to “Existence and regularity of minimizers of nonconvex integrals with p-q growth”

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.

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.

An existence result for a nonconvex variational problem via regularity

Irene Fonseca, Nicola Fusco, Paolo Marcellini (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The x -dependence, explicitly appearing in the integrands, adds significant technical difficulties in the...