非凸无界积分泛函的随机同调
Stochastic homogenization of nonconvex unbounded integral functionals with generalized Orlicz growth
AI总结：
本文研究了非凸无界随机积分泛函的随机同调理论，基于广义Orlicz型增长条件，提出了一种完整的同调理论框架，并在Musielak-Orlicz空间中定义了极限能量。
摘要：
我们考虑了可能无界的随机积分泛函的同化，即积分算子的定义域不一定是整个空间且可能依赖于空间变量。在向量情况下，我们开发了非凸无界泛函的完整随机同化理论，这些泛函具有广义Orlicz型的凸增长，基于该领域标准假设集，特别是阶数为p→−1的 coercivity 条件和阶数为p+<∞的上界条件。极限能量在可能各向异性的Musielak-Orlicz空间中定义，为此提供了光滑函数的近似结果。证明基于Γ-收敛的局部化方法和对截断论证的仔细使用。
英文摘要：
We consider the homogenization of random integral functionals which are possibly unbounded, that is, the domain of the integrand is not the whole space and may depend on the space-variable. In the vectorial case, we develop a complete stochastic homogenization theory for nonconvex unbounded functionals with convex growth of generalized Orlicz-type, under a standard set of assumptions in the field, in particular a coercivity condition of order $p^->1$, and an upper bound of order $p^+<\infty$. The limit energy is defined in a possibly anisotropic Musielak-Orlicz space, for which approximation results with smooth functions are provided. The proof is based on the localization method of $Γ$-convergence and a careful use of truncation arguments.
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