Rotationally symmetric p-harmonic flows from D^2 to S^2: local well-posedness and blow-up

Razvan Gabriel Iagar; Salvador Moll

paper

Rotationally symmetric p-harmonic flows from D^2 to S^2: local well-posedness and blow-up

arXiv:1305.6552

Abstract

We study the $p$ -harmonic flow from the unit disk $D^{2}$ to the unit sphere $S^{2}$ under rotational symmetry. We show that the Dirichlet problem with constant boundary conditions is locally well-posed in the class of classical solutions and we also give a sufficient criterion, in terms of the boundary condition, for the derivative of the solutions to blow-up in finite time.