Eigenfunction estimates on manifolds with boundary and applications to partial differential equations

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

Eigenfunction Estimates on Manifolds with Boundary and Applications to Partial Differential Equations Abstract of Proposed Research Xiangjin Xu This project is to study properties of the eigenfunctions of the Laplace-Beltrami operator on compact manifolds with boundary. Either zero Dirichlet or Neumann boundary data are imposed. Specific topics include L-p estimates, multiplier problems and convergence phenomena for eigenfunction expansions. Also bilinear and multilinear eigenfunction estimates for spectral projectors. Eigenfunction expansions are one of the primary tools in the analysis of partial differential equations in science and engineering. The results of this project will provide information that is important for the understanding of many scientific phenomena.