[lr4444lr]

I did state though that all second derivatives of u would have L^p norms bounded by that of the Laplacian. Kleinermann asked me for an elementary explanation of this, but I couldn't think of one.

I haven't the foggiest idea of what an "elementary explanation" of anything during a math graduate degree committee assessment would even sound like.

[teraflop]

"Elementary" is a somewhat subjective term that roughly means "from first principles", i.e. not relying on a bunch of advanced theorems and concepts. It doesn't necessarily mean the explanation is simple or concise.

[eru]

Often the advanced theorems and concepts make for a simpler and more concise explanation.

I guess the closest equivalent in programming is "implement X without using any external libraries (or perhaps only the standard library)".

[adgjlsfhk1]

Elementary number theory means that you are doing number theory without complex analysis or lots of abstract algebra

[NotYourLawyer]

Elementary means not using complex numbers.

[superposeur]

“Elementary” is a relative term!