May 2, 2015 · Okay this may sound stupid but I need a little help... What do $\\Large \\frac{d}{dx}$ and $\\Large \\frac{dy}{dx}$ mean? I need a thorough explanation. Thanks.

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Let $\\varphi(x,t)$ be a sufficiently smooth solution of the problem $$\\left\\{\\begin{array}{rcll} \\frac{\\partial\\varphi}{\\partial t}(x,t) - \\frac{\\partial^2 ...

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Why exactly are you looking for a lower bound? Are you looking for the exact value of the minimum? To (only) minimize the functional (prove the existence of a minimizer) you need …

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Update: Two things have happened: Rankeya has given a valid answer to the written question, but I realize now I was too vague. Secondly, I looked up the correct exercise in Jacobson and …

As noted in the comments, your derivation contains a mistake. To answer the question, this function can not be integrated in terms of elementary functions. So there is no "simple" answer …

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