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arXiv · 2309.00370

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

Jae-Hwan Choi·Jin Bong Lee·Jinsol Seo·Kwan Woo
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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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Jae-Hwan Choi, Jin Bong Lee, Jinsol Seo, Kwan Woo. 2023-09-01. On the trace theorem to Volterra-type equations with local or non-local derivatives. https://arxiv.org/abs/2309.00370

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