Potential theory studies harmonic functions, subharmonic functions, and the Laplace operator, including harmonic measure, regular boundary points, and the Dirichlet problem. The Brownian representation of the Dirichlet problem connects these analytic objects with exit probability distributions.
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Potential theory is a branch of mathematical analysis that deals with potentials and potential functions, typically in relation to fields such as electrostatics, gravitation, fluid dynamics, and various areas of applied mathematics. The theory is largely concerned with the behavior of harmonic functions and their properties. At its core, potential theory examines the concept of a potential function, which describes gravitational or electrostatic potentials in physics.