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I am currently figuring out what topic to work on for my undergraduate thesis and was able to narrow it down to mathematical analysis. As of now, I have two main options: a thesis working on Sobolev Embedding Theorems (more functional analysis) and one on variational elliptic problems in PDEs (which as I understand will focus more on proving the existence and uniqueness of solutions). I'm already studying Sobolev Spaces and its properties and the direction I take after this will differ based on what I choose. Unfortunately, both interest me equally which is why this continues to be a dificult decision to make.

So, I want to ask what writing or doing research on these topics are like? Is there a topic that's more important to learn as early as now for a student wanting to pursue graduate studies?

Thank you so much!

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    $\begingroup$ An undergraduate student starting research needs an adviser. I suppose you have one. Ask him/her. $\endgroup$ Nov 24 at 15:29
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    $\begingroup$ Variational methods for solving nonlinear elliptic PDEs often use Sobolev spaces and inequalities. I suggest you pick one that does. $\endgroup$
    – Deane Yang
    Nov 24 at 16:20

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