We consider non-autonomous functionals of the form F(u,ω) = int_ω f(x,Du(x))dx,where u : ω →ℝ^N , ω subset ℝ^n . We assume that f(x, z) grows at least as |z|^p and at most as |z|^q.Moreover, f(x, z) is Holder continuous with respect to x and convex with respect to z. In this setting, we give a sufficient condition on the density f(x, z) that ensures the absence of a Lavrentiev gap..
Absence of Lavrentiev gap for non-autonomous functionals with (p,q)-growth
Leonetti, Francesco;
2019-01-01
Abstract
We consider non-autonomous functionals of the form F(u,ω) = int_ω f(x,Du(x))dx,where u : ω →ℝ^N , ω subset ℝ^n . We assume that f(x, z) grows at least as |z|^p and at most as |z|^q.Moreover, f(x, z) is Holder continuous with respect to x and convex with respect to z. In this setting, we give a sufficient condition on the density f(x, z) that ensures the absence of a Lavrentiev gap..File in questo prodotto:
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