In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equations, where uniform trace estimates on the half-line are shown.
On the trace embedding and its applications to evolution equations / Agresti, Antonio; Lindemulder, Nick; Veraar, Mark. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 296:4(2023), pp. 1319-1350. [10.1002/mana.202100192]
On the trace embedding and its applications to evolution equations
Agresti, Antonio;
2023
Abstract
In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpolation couples. The abstract results are applied to regularity problems for fractional evolution equations and stochastic evolution equations, where uniform trace estimates on the half-line are shown.| File | Dimensione | Formato | |
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