Elliptic systems of higher order with critical nonlinearity

在Rivière、Struwe和Lamm最近的工作中，具有临界非线性的二阶或四阶拟线性椭圆组弱解的正则性理论被推到了一个新的水平。对于高阶系统(散度形式)，还缺乏类似的一般理论。在我们的项目中，我们希望从关键维度考虑问题开始。这可能会涉及到前面提到的方法，结合允许处理预期发生的负可微性的Soblev空间的论点。

The regularity theory for weak solutions of quasilinear elliptic systems of second or fourth order with critical nonlinearity has been pushed to new levels in recent work by Rivière, Struwe, and Lamm. A similarly general theory for systems of higher order (in divergence form) is still lacking. In our project, we would like to start it with considering the problem in the critical dimension. This will probably involve the methods mentioned, combined with arguments which allow handling the Sobolev spaces of negative differentiability that are expected to occur.