On a class of quasilinear operators on smooth metric measure spaces

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.

Comments are welcome. 36 pages

References in corpus (1)

• Sharp lower bound for the first eigenvalue of the Weighted $p$-Laplacian