论文标题
Liouville型定理用于半空间中椭圆方程的无限解决方案
Liouville-type theorems for unbounded solutions of elliptic equations in half-spaces
论文作者
论文摘要
我们证明，半空间中车道束方程的差异问题没有正面的解决方案，最多像方程式自然缩放指数给出的边界的距离距离距离距离距离距离距离距离最大。换句话说，我们排除{\ it type〜i i的增长}解决方案。以前仅适用于有界解决方案，或在非线性中的功率限制下，这种不存在的结果以前可用。在证明方面的工具是解决方案的对数梯度及其正常衍生物的局部方向界限，这也是我们也确定的。
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solutions which grow at most like the distance to the boundary to a power given by the natural scaling exponent of the equation; in other words, we rule out {\it type~I grow-up} solutions. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. Instrumental in the proof are local pointwise bounds for the logarithmic gradient of the solution and its normal derivative, which we also establish.
