Reverse bubbling of currents and harmonic heat flows with prescribed singular set

Adriano Pisante
April 2004
Calculus of Variations & Partial Differential Equations;Apr2004, Vol. 19 Issue 4, p337
Academic Journal
We consider the harmonic heat flow for maps u between B 3, the unit ball of $\mathbb{R}^3$ , and its boundary S 2. For a class of possibly singular initial and boundary data we show the existence of a weak solution whose singular set is a fixed discrete set on the vertical axis arbitrarily prescribed. Other examples including isolated singularities moving along a prescribed trajectory are given.


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