Harmonic functions and the classical Dirichlet problem

23 Fevereiro 2017, 11:00 • Hugo Tavares

Harmonic functions and the classical Dirichlet problem [GT, 13-16]: Mean value properties and the maximum/minimum principle for sub/superharmonic functions; the Harnack inequality; [E, 29-41]: local estimates for harmonic functions and the Liouville theorem; Green function and representation formula for solution of the Dirichlet problem for the Poisson equation; the explicit classical solutions in the half-space and in the Ball via Poisson integrals [GT, 23-27] brief introduction to the Perron method for the solution of the Dirichlet problem with continuous data on boundaries with regular points See also [S,141-147].