Fritz Gesztesy (University of Missouri)
Positivity Preserving Operators and Heat Kernel Bounds for 2nd Order Elliptic Partial Differential Operators with Robin-type Boundary Conditions
Exploiting the notions of positivity preserving linear operators and operator domination, we establish Gaussian upper bounds for the heat kernels of 2nd order elliptic partial differential operators in divergence form on bounded Lipschitz domains with (generally, non-local) Robin-type boundary conditions. Green's function estimates are also discussed.
This talk is based on joint work with Marius Mitrea and Roger Nichols.