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<p>We characterize the Hölder regularity in time of classical solutions for a class of nonlocal abstract equations in terms of resolvent estimates of the underlying operator, thus including in our approach those recently incorporated into the literature that study nonlocal versions of the Moore-Gibson-Thompson equation. This allows us to prove new maximal regularity results, including a priori estimates. Our results are flexible enough to allow the admissibility of operators other than the Laplacian. Furthermore, the presented method is reliable enough to apply these techniques to other nonlocal abstract equations of interest, obtain similar results and promote new findings.</p>

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Hölder continuous solutions for tempered fractional equations and maximal regularity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月20日

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  • Edgardo Alvarez,
  • Carlos Lizama,
  • Marina Murillo-Arcila

摘要

We characterize the Hölder regularity in time of classical solutions for a class of nonlocal abstract equations in terms of resolvent estimates of the underlying operator, thus including in our approach those recently incorporated into the literature that study nonlocal versions of the Moore-Gibson-Thompson equation. This allows us to prove new maximal regularity results, including a priori estimates. Our results are flexible enough to allow the admissibility of operators other than the Laplacian. Furthermore, the presented method is reliable enough to apply these techniques to other nonlocal abstract equations of interest, obtain similar results and promote new findings.