论文标题
非紧凑型鳍片歧管上的关键椭圆方程
Critical elliptic equations on non-compact Finsler manifolds
论文作者
论文摘要
在本文中，我们处理了一个准线性椭圆方程，该方程涉及非紧凑型兰德斯空间上的关键Sobolev指数。在对扰动的非常普遍的假设下，我们证明了非平凡解决方案的存在。该方法基于变化的算法的直接方法。关键步骤之一是证明与该问题相关的能量功能在Sobolev空间的小球上的半连续性较弱，这是由一般不等式提供的。
In the present paper, we deal with a quasilinear elliptic equation involving a critical Sobolev exponent on non-compact Randers spaces. Under very general assumptions on the perturbation, we prove the existence of a non-trivial solution. The approach is based on the direct methods of the calculus of variations. One of the key steps is to prove that the energy functional associated with the problem is weakly lower semicontinuous on small balls of the Sobolev space, which is provided by a general inequality.
