论文标题
对椭圆形问题的解决方案的尖锐估计值混合边界条件
Sharp estimates for solutions to elliptic problems with mixed boundary conditions
论文作者
论文摘要
我们使用对称化技术表明，可以证明比较原理（我们主要集中在$ l^1 $比较上）与椭圆形偏微分方程之间的解决方案之间具有相当通用的边界条件$ω$的椭圆形偏微分方程，并且解决了相当通用的边界条件的解决方案，并且解决方案在与$ω$相同的球上定义的适当相关问题的解决方案。这包括例如在边界的一部分处方Dirichlet边界条件的混合问题，而Robin边界条件则在其补体中规定。
We show, using symmetrization techniques, that it is possible to prove a comparison principle (we are mainly focused on $L^1$ comparison) between solutions to an elliptic partial differential equation on a smooth bounded set $Ω$ with a rather general boundary condition, and solutions to a suitable related problem defined on a ball having the same volume as $Ω$. This includes for instance mixed problems where Dirichlet boundary conditions are prescribed on part of the boundary, while Robin boundary conditions are prescribed on its complement.
