Let $F:M\to \mathbb R^N$ be an embedding. This embedding induces a metric $g_F=dF\cdot dF$ on $M$, that turns $F$ into an isometric embedding. Probably the hardest part of the proof of the Nash ...
I heard that De Giorgi-Nash-Moser type regularity arguments fail for elliptic systems, but do not know where to start looking for more substantial information. Why does the regularity fail? Is there ...