论文标题
关于4谐波和ES-4谐波地图的有限能量解决方案
On finite energy solutions of 4-harmonic and ES-4-harmonic maps
论文作者
论文摘要
4-谐波和ES-4谐波图是研究良好的谐波方程的两个概括，这两者都由第八阶的非线性椭圆部分微分方程给出。由于衍生品的数量很大，很难在这两个变异问题的定性行为上找到任何差异。在本文中，我们证明，来自欧几里得空间的4谐波和ES-4谐波图的有限能量解决方案必须微不足道。但是，对于4谐波和ES-4谐波地图，我们需要有限的能量有所不同，指出这两个变化问题之间的第一个差异。
4-harmonic and ES-4-harmonic maps are two generalizations of the well-studied harmonic map equation which are both given by a nonlinear elliptic partial differential equation of order eight. Due to the large number of derivatives it is very difficult to find any difference in the qualitative behavior of these two variational problems. In this article we prove that finite energy solutions of both 4-harmonic and ES-4-harmonic maps from Euclidean space must be trivial. However, the energy that we require to be finite is different for 4-harmonic and ES-4-harmonic maps pointing out a first difference between these two variational problems.
