31-XX Potential theory {For probabilistic potential theory, see 60J45}
31-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
31-01 Instructional exposition (textbooks, tutorial papers, etc.)
31-02 Research exposition (monographs, survey articles)
31-03 Historical {!must also be assigned at least one classification number from section 01}
31-04 Explicit machine computation and programs (not the theory of computation or programming)
31-06 Proceedings, conferences, collections, etc.
31Axx Two-dimensional theory
31A05 Harmonic, subharmonic, superharmonic functions
31A10 Integral representations, integral operators, integral equations methods
31A15 Potentials and capacity, harmonic measure, extremal length [See also 30C85]
31A20 Boundary behavior (theorems of Fatou type, etc.)
31A25 Boundary value and inverse problems
31A30 Biharmonic, polyharmonic functions and equations, Poisson's equation
31A35 Connections with differential equations
31A99 None of the above, but in this section
31Bxx Higher-dimensional theory
31B05 Harmonic, subharmonic, superharmonic functions
31B10 Integral representations, integral operators, integral equations methods
31B15 Potentials and capacities, extremal length
31B20 Boundary value and inverse problems
31B25 Boundary behavior
31B30 Biharmonic and polyharmonic equations and functions
31B35 Connections with differential equations
31B99 None of the above, but in this section
31Cxx Other generalizations
31C05 Harmonic, subharmonic, superharmonic functions
31C10 Pluriharmonic and plurisubharmonic functions [See also 32U05]
31C12 Potential theory on Riemannian manifolds [See also 53C20] {For Hodge theory, see 58A14}
31C15 Potentials and capacities
31C20 Discrete potential theory and numerical methods
31C25 Dirichlet spaces
31C35 Martin boundary theory [See also 60J50]
31C40 Fine potential theory
31C45 Other generalizations (nonlinear potential theory, etc.)
31C99 None of the above, but in this section
31D05 Axiomatic potential theory