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

Citation:

Guangsheng YU,Mati ur RAHMAN,Yingshu L¨U.Continuity of Almost Harmonic Maps with the Perturbation Term in a Critical Space[J].Chinese Annals of Mathematics B,2022,43(4):585~600
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Authors:

Guangsheng YU; Mati ur RAHMAN;Yingshu L¨U
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) Ln/2 logq L, n is the dimension with n ≥ 3. They prove that when q > n/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

Classification:

58E20, 35B65, 35J60, 35S05, 35S15
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