Continuity of almost harmonic maps with the perturbation term in a critical space (Q2082272)

The authors study the continuity estimate of the solutions of almost harmonic maps with the perturbation term \(f\) in a critical integrability class (Zygmund class) \(L^{\frac{n}{2}}\log^q L\), where \(n\) is the dimension, \(n\ge3\). It is shown that for \(q>\frac{n}{2}\), the solution must be continuous, and continuity modulus estimates can be provided. Finally, boundary continuity for the almost harmonic maps in high dimension is studied, as well.