Continuity of Almost Harmonic Maps with the Perturbation Term in a Critical Space

Abstract

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) ${L^{{n \over 2}}}$, log ^q L, n is the dimension with n ≥ 3. They prove that when $q > {n \over 2}$ the solution must be continuous and they can get continuity modulus estimates. As a byproduct of their method, they also study boundary continuity for the almost harmonic maps in high dimension.

Keywords

Harmonic maps / Nonlinear elliptic PDE / Boundary regularity

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