u subharmonic if Δu ≥ 0. Maximum-principle: u attains max on boundary. Perron envelope = sup over subharmonics ≤ g on boundary solves Dirichlet problem. Foundation for non-classical solutions to elliptic PDEs.
u subharmonic if Δu ≥ 0. Maximum-principle: u attains max on boundary. Perron envelope = sup over subharmonics ≤ g on boundary solves Dirichlet problem. Foundation for non-classical solutions to elliptic PDEs.