Published Paper

Inserted: 23 jan 2024
Last Updated: 23 jan 2024

Journal: Calculus of Variations and Partial Differential Equations
Volume: 63
Year: 2024
Doi: 10.1007/s00526-023-02640-1
Links: doi

Abstract:

We study classes of weights ensuring the absence and presence of the Lavrentiev's phenomenon for double phase functionals upon every choice of exponents. We introduce a new sharp scale for weights for which there is no Lavrentiev's phenomenon up to a counterexample we provide. This scale embraces the sharp range for $\alpha$-Hölder continuous weights. Moreover, it allows excluding the gap for every choice of exponents $q,p>1$.

Keywords: calculus of variations, Lavrentiev’s phenomenon, double-phase functionals, relaxation methods