论文标题
在平滑度量空间上的一类准线性操作员上
On a class of quasilinear operators on smooth metric measure spaces
论文作者
论文摘要
对于平滑度量测量空间（如果边界是非空的），我们在平滑度量度量空间上的大型准同性恋抛物线方程的解决方案的溶液中得出了对连续性模量的尖锐估计。我们还为一类均质的准算子操作员的第一个dirichlet特征值提供了最佳的下限，其中包括非相位操作员。主要特征是该类别的运营商具有相应的一维操作员，这可以与一维方程的解决方案进行彻底的比较。
We derive sharp estimates on the modulus of continuity for solutions of a large class of quasilinear isotropic parabolic equations on smooth metric measure spaces (with Dirichlet or Neumann boundary condition in case the boundary is non-empty). We also derive optimal lower bounds for the first Dirichlet eigenvalue of a class of homogeneous quasilinear operators, which include non-variational operators. The main feature is that this class of operators have corresponding one-dimensional operators, which allow sharp comparisons with solutions of one-dimensional equations.
