This article extends the celebrated Sewing lemma, known from the theory of rough paths, to multi-parameter fields on hyper-cubes. We use this to construct Young integrals for multi-parameter Hölder fields on general domains \(\left[ 0,T\right] ^{k}\) with \(k\ge 1\) taking values in \({\mathbb {R}}^{d}\). Moreover, we show existence, uniqueness and stability of some particular types of hyperbolic SPDEs driven by space-time Hölder noise in a Young regime.

中文翻译：

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将缝纫引理扩展到由多参数Young场驱动的超立方体和双曲方程

本文将从粗糙路径理论中得知的著名缝纫引理扩展到超立方体上的多参数场。我们使用它来构造通用域\（\ left [0，T \ right] ^ {k} \）上多参数Hölder字段的Young积分，其中\（k \ ge 1 \）取\（{\ mathbb {R}} ^ {d} \）。此外，我们展示了在扬格体制中由时空霍尔德噪声驱动的某些特定类型的双曲SPDE的存在，唯一性和稳定性。