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<p>We extend the semigroup approach used in Hoshino (<a href="https://arxiv.org/abs/2310.07396">https://arxiv.org/abs/2310.07396</a>, 2019); Otto and Weber (Arch Ration Mech Anal 232:873–950, 2019) to provide alternative proofs of the reconstruction theorem and the multilevel Schauder estimate for singular modelled distributions. As an application of them, we construct the local-in-time solution of the two dimensional parabolic Anderson model with a non-translation invariant differential operator.</p>

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A semigroup approach to the reconstruction theorem and the multilevel Schauder estimate for singular modelled distributions

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Masato Hoshino,
  • Ryoji Takano

摘要

We extend the semigroup approach used in Hoshino (https://arxiv.org/abs/2310.07396, 2019); Otto and Weber (Arch Ration Mech Anal 232:873–950, 2019) to provide alternative proofs of the reconstruction theorem and the multilevel Schauder estimate for singular modelled distributions. As an application of them, we construct the local-in-time solution of the two dimensional parabolic Anderson model with a non-translation invariant differential operator.