 Perron method

The Perron method constructs a harmonic solution with prescribed boundary data as the pointwise supremum of all subharmonic functions lying below those data. Harmonic lifting proves interior harmonicity; barriers determine whether the supremum attains the boundary values.

The Perron method typically refers to techniques associated with the Perron-Frobenius theorem in the context of linear algebra and the study of non-negative matrices and certain types of dynamical systems. The theorem has important implications in various fields, such as economics, graph theory, and the study of Markov chains.