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On the trace theorem to Volterra-type equations with local or non-local derivatives

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arxiv 2309.00370 v2 pith:NRURC7DX submitted 2023-09-01 math.AP

Jae-Hwan Choi , Jin Bong Lee , Jinsol Seo , Kwan Woo This is my paper · ORCID
classification math.AP
keywords equationsderivativesgeneralizedinterpolationlocalnon-localtheorytrace
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abstract

This paper considers traces at the initial time for solutions of evolution equations with local or non-local derivatives in vector-valued $L_p$ spaces with $A_p$ weight. To achieve this, we begin by introducing a generalized real interpolation method. Within the framework of generalized interpolation theory, we make use of stochastic process theory and two-weight Hardy's inequality to derive our trace and extension theorems. Our results encompass findings applicable to time-fractional equations with broad temporal weight functions.

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Cited by 2 Pith papers

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  1. A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces

    math.AP 2025-12 accept novelty 6.0 of 10

    A weighted mixed-norm Sobolev-Zygmund regularity theorem for second-order parabolic equations with time-measurable, spatially Zygmund coefficients, including nonzero initial data in the optimal trace space.

  2. Nonlinear SPDEs and Maximal Regularity: An Extended Survey

    math.PR 2025-01 conditional novelty 4.0 of 10

    A survey with new extensions of the maximal-regularity framework for nonlinear SPDEs, yielding local well-posedness, blow-up criteria, and instantaneous regularization in critical spaces.

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