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Results tagged with fa.functional-analysis
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user 100894
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
0
votes
1
answer
72
views
Moreau-Enveloppe from $L^2(0,T;V) \to L^2(0,T;V^*)$
Let $V,H,V^*$ be a Gelfand-Triple, $\phi\colon V \to \mathbb{R}$ convex, lower semicontinuous and proper. There exists a so called Moreau-Enveloppe $\phi_j$, which is Gateâux-differentialable. It's de …
- 187
1
vote
0
answers
48
views
Verifying general assumption for parabolic PDE
I've got some problems verifying an assumption for a parabolic PDE. Namely, let $(V,H,V^*)$ be a Gelfand-Triple, $u_0 \in V$, $\psi\colon V \to \mathbb{R}$ convex and lower-semicontinuous and $a\colon …
- 187
2
votes
1
answer
446
views
Derivative of Yosida-Approximation
i have got a problem with some assumptions to solve a parabolic variational inequality. My Problem is: Find a function $u$ with
\begin{align}
u\in L^2(0,T;V),~ u' \in L^2(0,T;V') \\
(u'(t),v-u(t)) + …
- 187
2
votes
1
answer
590
views
Strong convergence of differential quotient in $L^2(0,T;V^*)$
I have got a problem regarding the weak differentiability of Bochner-integrable functions. Let $(V,H,V^*)$ be a Gelfand-triple and
\begin{align*}
w \in W(0,T) := \{w\in L^2(0,T;V) ~\vert~ \exists w' …
- 187