On the trace theorem to Volterra-type equations with local or non-local derivatives
| Autor: | Choi, Jae-Hwan, Lee, Jin Bong, Seo, Jinsol, Woo, Kwan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: few glitches corrected, Appendix B for finite time case added |
| Databáze: | arXiv |
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