Absence of Lavrentiev gap for non-autonomous functionals with (p, q)-growth

Esposito A, Leonetti F, Petricca PV (2019)


Publication Language: English

Publication Status: Published

Publication Type: Journal article

Publication year: 2019

Journal

Publisher: WALTER DE GRUYTER GMBH

Book Volume: 8

Pages Range: 73-78

Journal Issue: 1

DOI: 10.1515/anona-2016-0198

Abstract

We consider non-autonomous functionals of the form F(u, Omega) =integral(Omega) f(x, Du(x))dx, where u : Omega -> R-N, Omega subset of R-n. We assume that f(x, z) grows at least as vertical bar z vertical bar(p) and at most as vertical bar z vertical bar(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.

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APA:

Esposito, A., Leonetti, F., & Petricca, P.V. (2019). Absence of Lavrentiev gap for non-autonomous functionals with (p, q)-growth. Advances in Nonlinear Analysis, 8(1), 73-78. https://dx.doi.org/10.1515/anona-2016-0198

MLA:

Esposito, Antonio, Francesco Leonetti, and Pier Vincenzo Petricca. "Absence of Lavrentiev gap for non-autonomous functionals with (p, q)-growth." Advances in Nonlinear Analysis 8.1 (2019): 73-78.

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