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arXiv · 2303.05877

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

Michał Borowski·Iwona Chlebicka·Filomena De Filippis·Błażej Miasojedow
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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 $\alpha$-H\"older continuous weights. Moreover, it allows excluding the gap for every choice of exponents $q,p>1$.

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Michał Borowski, Iwona Chlebicka, Filomena De Filippis, Błażej Miasojedow. 2023-03-10. Absence and presence of Lavrentiev's phenomenon for double phase functionals upon every choice of exponents. https://arxiv.org/abs/2303.05877

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