Dirichlet-to-Neumann Map for the p-Laplacian on Metric Measure Spaces

Explore advanced mathematical concepts in this 53-minute seminar talk from the Spectral Geometry in the Clouds series. Delve into Ryan Gibara's research on the Dirichlet-to-Neumann map for the p-Laplacian in metric measure spaces. Examine the construction of this map in bounded, locally compact, uniform domains with doubling measures supporting p-Poincaré inequalities. Investigate the relationship between Newton-Sobolev spaces and their boundary trace classes, identified as Besov function spaces. Analyze the implications for Dirichlet and Neumann problems with Besov boundary data and its dual space. Gain insights into this collaborative work with Nageswari Shanmugalingam, exploring advanced topics in spectral geometry and functional analysis.