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On the trace embedding and its applications to evolution equations |
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| Authors: | Antonio Agresti Nick Lindemulder Mark Veraar |
| Institution: | 1. Institute of Science and Technology Austria, Klosterneuburg, Austria;2. Institute of Analysis, Karlsruhe Institute of Technology, Karlsruhe, Germany;3. Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands |
| 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. |
| Keywords: | anisotropic function spaces Bessel-potential spaces Besov spaces integral equations Sobolev spaces stochastic maximal regularity traces Triebel–Lizorkin spaces weighted function spaces |