论文标题
椭圆形偏微分方程解决方案的径向限制
Radial limits of solutions to elliptic partial differential equations
论文作者
论文摘要
对于某些椭圆形差分运算符$ l，我们研究解决方案到$ lu = 0的行为，$，因为我们倾向于在$ \ r^n，n \ ge 3中沿着严格的恒星型域沿着半径沿着边界3。$类似的结果是在其他特殊域中获得的。我们的方法涉及引入谐波线束作为脑谐波空间的实例，并通过适当的子集对谐波函数近似函数近似。这些谐波空间上的这些近似定理产生了有趣的示例，以通过$ \ r^n。
For certain elliptic differential operators $L,$ we study the behaviour of solutions to $Lu=0,$ as we tend to the boundary along radii in strictly starlike domains in $\R^n, n\ge 3.$ Analogous results are obtained in other special domains. Our approach involves introducing harmonic line bundles as instances of Brelot harmonic spaces and approximating continuous functions by harmonic functions on appropriate subsets. These approximation theorems on harmonic spaces yield interesting examples for approximation by solutions of $Lu=0$ on some domains in $\R^n.$
