We study the integral representation properties of limits of sequences of integral functionals 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,Du) depending explicitly on u; finally we weaken the assumption allowing p(x) to be discontinuous on nice sets.
Integral representation and Gamma-convergence of variational integrals with p(x)-growth / Coscia, Alessandra; Mucci, Domenico. - In: ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. - ISSN 1262-3377. - 7:21(2002), pp. 495-519. [10.1051/cocv:2002065]
Integral representation and Gamma-convergence of variational integrals with p(x)-growth
MUCCI, Domenico
2002
Abstract
We study the integral representation properties of limits of sequences of integral functionals 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,Du) depending explicitly on u; finally we weaken the assumption allowing p(x) to be discontinuous on nice sets.
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