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Results tagged with fa.functional-analysis
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user 52874
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
0
answers
134
views
Comparison principle using truncation for porous medium equation
For a porous medium equation (eg. $u_t - \Delta \Phi(u) = f$), is it possible to obtain a comparison principle for very weak solutions (eg. if $u_0 \geq 0$ and $f \geq 0$ then $u \geq 0$ a.e.) using t …
- 43
3
votes
1
answer
214
views
Lower semicontinuity of a Bochner integral of a convex function
I'm looking for the following result:
Let $\Omega \subset \mathbb{R}^n$ be a bounded domain. The map
$$u \mapsto \int_0^T \int_{\Omega} f(u(t))$$
is lower semicontinuous for $u \in L^2(0,T;L^2 …
- 43