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

  • Alessandra Coscia (a1) and Domenico Mucci (a1)

Abstract

We study the integral representation properties of limits of sequences of integral functionals like   $\int f(x,Du)\,{\rm d}x$   under nonstandard growth conditions of (p,q)-type: namely, we assume that $$ \vert z\vert^{p(x)}\leq f(x,z)\leq L(1+\vert z\vert^{p(x)})\,. $$ 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,Du) depending explicitly on u; finally we weaken the assumption allowing p(x) to be discontinuous on nice sets.

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

  • Alessandra Coscia (a1) and Domenico Mucci (a1)

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