论文标题
Orlicz-Sobolev的不平等和无限退化椭圆运算符的Dirichlet问题
Orlicz-Sobolev inequalities and the Dirichlet problem for infinitely degenerate elliptic operators
论文作者
论文摘要
我们研究了无限退化椭圆操作员的Dirichlet问题的解决性与相关亚基公制空间中Orlicz-Sobolev不等式的有效性。对于亚细算子来说，众所周知，经典的Sobolev不等式足以且几乎需要使用溶液上的定量绑定来解决Dirichlet问题[11]。当堕落是无限类型时，较弱的Orlicz-Sobolev不平等似乎是正确的替代品[7]。在本文中，我们进一步研究了这一联系，并减少了必要条件和足够条件之间的差距，以解决Dirichlet问题。
We investigate a connection between solvability of the Dirichlet problem for an infinitely degenerate elliptic operator and the validity of an Orlicz-Sobolev inequality in the associated subunit metric space. For subelliptic operators it is known that the classical Sobolev inequality is sufficient and almost necessary for the Dirichlet problem to be solvable with a quantitative bound on the solution [11]. When the degeneracy is of infinite type, a weaker Orlicz-Sobolev inequality seems to be the right substitute [7]. In this paper we investigate this connection further and reduce the gap between necessary and sufficient conditions for solvability of the Dirichlet problem.
