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edited Jan 25, 2021 at 15:20

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fa.functional-analysis ap.analysis-of-pdes sobolev-spaces traces interpolation-spaces

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edited Jan 24, 2021 at 19:30

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fa.functional-analysis ap.analysis-of-pdes sobolev-spaces traces trace-formula

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asked Jan 24, 2021 at 16:43

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Trace of a function

Let $T,L> 0$ two real numbers and we consider the Sobolev space $X := L^2(0,T; H^1(0,L))\cap H^{1}(0,T;H^{-1}(0,L))$. My question is:

Given $f \in X$, the trace $ t \mapsto f(t,L)$ belongs to what space? Could someone indicate me a reference?

fa.functional-analysis ap.analysis-of-pdes sobolev-spaces traces trace-formula