发表机构
Kyungpook National University（庆北国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明具有Orlicz增长的一般类抛物双相泛函中拉夫连季耶夫现象缺失，将相关理论从幂次增长扩展到广泛Young函数框架，确定了问题对应的时空Orlicz能量类。
AI 中文摘要
本文证明了具有Orlicz增长的一般类抛物双相泛函中拉夫连季耶夫现象的缺失。能量密度由$$ G(|Dw|)+a(x,t)H(|Dw|) $$给出，其中$G$和$H$是满足$\nabla_2$和$\nabla_2$条件且$G\boldsymbol{\nless} H$的Young函数，$a(\boldsymbol{\ncdot})$是连续非负系数。在$G$与$H$的增长间隙和$a(\boldsymbol{\ncdot})$的连续性模之间的适当平衡条件下，我们证明每个有限能量映射都可以在不损失能量的情况下被光滑函数局部逼近。该结果将已知的抛物双相理论从幂次增长扩展到广泛的Young函数框架，并确定了该问题的自然时空Orlicz能量类。
英文摘要
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 $\nabla_2$ conditions with $G\prec H$, and $a(\cdot)$ is a continuous nonnegative coefficient. Under suitable balance conditions between the growth gap of $G$ and $H$ and the modulus of continuity of $a(\cdot)$, 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.
