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Absence of the Lavrentiev phenomenon for a general class of parabolic double phase problems
Abstract
In this paper, we prove the absence of the Lavrentiev phenomenon for a general class of parabolic double phase functionals with Orlicz growth. The energy density is given by G(|Dw|)+a(x,t)H(|Dw|), where G and H are Young functions satisfying the Δ2 and ∇2 conditions with G≺ H, and a(·) is a continuous nonnegative coefficient. Under suitable balance conditions between the growth gap of G and H and the modulus of continuity of a(·), we show that every finite-energy map can be approximated locally by smooth functions without loss of energy. The result extends the known parabolic double phase theory from power type growth to a broad Young function framework and identifies the natural space-time Orlicz energy class for the problem.
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BibTeX
@misc{kim2026absence,
title = {{Absence of the Lavrentiev phenomenon for a general class of parabolic double phase problems}},
author = {Youngchae Kim and Jehan Oh},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29085},
eprint = {2608.29085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29085},
}
RIS
TY - UNPB
TI - Absence of the Lavrentiev phenomenon for a general class of parabolic double phase problems
AU - Youngchae Kim
AU - Jehan Oh
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29085
UR - https://arxiv.org/abs/2608.29085
AB - In this paper, we prove the absence of the Lavrentiev phenomenon for a general class of parabolic double phase functionals with Orlicz growth. The energy density is given by G(|Dw|)+a(x,t)H(|Dw|), where G and H are Young functions satisfying the Δ_2 and ∇_2 conditions with G≺ H, and a(·) is a continuous nonnegative coefficient. Under suitable balance conditions between the growth gap of G and H and the modulus of continuity of a(·), we show that every finite-energy map can be approximated locally by smooth functions without loss of energy. The result extends the known parabolic double phase theory from power type growth to a broad Young function framework and identifies the natural space-time Orlicz energy class for the problem.
ER -