On a class of quasilinear operators on smooth metric measure spaces

Xiaolong Li; Yucheng Tu; Kui Wang

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arXiv · 2009.10418

On a class of quasilinear operators on smooth metric measure spaces

Xiaolong Li·Yucheng Tu·Kui Wang

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Abstract

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.

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Xiaolong Li, Yucheng Tu, Kui Wang. 2020-09-22. On a class of quasilinear operators on smooth metric measure spaces. https://arxiv.org/abs/2009.10418

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