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No Lavrentiev gap for some double phase integrals

  • Filomena De Filippis and Francesco Leonetti ORCID logo EMAIL logo
Published/Copyright: August 30, 2022

Abstract

We prove the absence of the Lavrentiev gap for non-autonomous functionals

( u ) Ω f ( x , D u ( x ) ) 𝑑 x ,

where the density f ( x , z ) is α-Hölder continuous with respect to x Ω n , it satisfies the ( p , q ) -growth conditions

| z | p f ( x , z ) L ( 1 + | z | q ) ,

where 1 < p < q < p ( n + α n ) , and it can be approximated from below by suitable densities f k .

MSC 2010: 35B65; 35J60; 35J47

Communicated by Frank Duzaar


Funding statement: Support from UnivAQ, MIUR, GNAMPA, INdAM is acknowledged.

Acknowledgements

The authors thank the referees for useful remarks that improved the final version.

References

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Received: 2021-12-21
Revised: 2022-04-11
Accepted: 2022-04-21
Published Online: 2022-08-30
Published in Print: 2024-01-01

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