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## Solution to Problem 3

So this problem comes from the functional analysis course I took last semester. Although simple, I thought was pretty cool. In the actual exercise they had broken it down into three parts, which I did not show in the problem post. Here I will show the steps as claims....

## Principles: Open Mapping Theorem

So guess what happened again, another WordPress malfunction… something really isn’t right here. The blog post is attached! Open Mapping BlogDownload

## Problem of the Week 3

Supposed that $u, f\in L^2(\Omega)$ satisfies $$\int_{\Omega}u\Delta^2 \phi^2 = \int_{\Omega} f\phi dx,$$ for all $\phi \in A = \{u\in H^4\cap H^1_0 (\Omega) : ~\Delta u \in H^1_0(\Omega)\}$. Prove that $u\in A$.

## Solution to Problem of the Week 2

So once again, WordPress doesn’t like my Latex, so I have attached this blog as a pdf. Enjoy! PrbWk2Download

## Solution to Problem of the Week 1

So for some reason my usual way of writing Latex on the blog doesn’t work for this post. I have no idea why unfortunately, so I will just add the post as a PDF attached to this! Solution to Problem 1Download