Absence and presence of Lavrentiev's phenomenon for double phase functionals upon every choice of exponents

2023/03/10 by Borowski, Michał, Chlebicka, Iwona, De Filippis, Filomena +1 · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.05877

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 α-Hölder continuous weights. Moreover, it allows excluding the gap for every choice of exponents q,p>1.

Cited by

• Gradient higher integrability of bounded solutions to parabolic double-phase systems
• Higher integrability for parabolic PDEs with generalized Orlicz growth
• Smoothness of weight sharply discards Lavrentiev's gap for double phase functionals

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