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- Potential_theory abstract "In mathematics and mathematical physics, potential theory is the study of harmonic functions.The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which satisfy Laplace's equation. Although more accurate theories - for example classical Electrostatics and Newtonian gravity - were developed later, the name "potential theory" remained.There is considerable overlap between potential theory and the theory of the Laplace equation. To the extent that it is possible to draw a distinction between these two fields, the difference is more one of emphasis than subject matter and rests on the following distinction: potential theory focuses on the properties of the functions as opposed to the properties of the equation. For example, a result about the singularities of harmonic functions would be said to belong to potential theory whilst a result on how the solution depends on the boundary data would be said to belong to the theory of the Laplace equation. Of course, this is not a hard and fast distinction, and in practice there is considerable overlap between the two fields, with methods and results from one being used in the other.Modern potential theory is also intimately connected with probability and the theory of Markov chains. In the continuous case, this is closely related to analytic theory. In the finite state space case, this connection can be introduced by introducing an electrical network on the state space, with resistance between points inversely proportional to transition probabilities and densities proportional to potentials. Even in the finite case, the analogue I-K of the Laplacian in potential theory has its own maximum principle, uniqueness principle, balance principle, and others.".
- Potential_theory wikiPageID "1431342".
- Potential_theory wikiPageRevisionID "603138322".
- Potential_theory author "A.I. Prilenko, E.D. Solomentsev".
- Potential_theory author "E.D. Solomentsev".
- Potential_theory hasPhotoCollection Potential_theory.
- Potential_theory id "6659".
- Potential_theory id "p/p074140".
- Potential_theory id "p/p074150".
- Potential_theory title "Abstract potential theory".
- Potential_theory title "Potential Theory".
- Potential_theory title "Potential theory".
- Potential_theory subject Category:Mathematical_physics.
- Potential_theory subject Category:Partial_differential_equations.
- Potential_theory subject Category:Potential_theory.
- Potential_theory type Abstraction100002137.
- Potential_theory type Communication100033020.
- Potential_theory type DifferentialEquation106670521.
- Potential_theory type Equation106669864.
- Potential_theory type MathematicalStatement106732169.
- Potential_theory type Message106598915.
- Potential_theory type PartialDifferentialEquation106670866.
- Potential_theory type PartialDifferentialEquations.
- Potential_theory type Statement106722453.
- Potential_theory comment "In mathematics and mathematical physics, potential theory is the study of harmonic functions.The term "potential theory" was coined in 19th-century physics, when it was realized that the fundamental forces of nature could be modeled using potentials which satisfy Laplace's equation.".
- Potential_theory label "Potentiaaltheorie".
- Potential_theory label "Potential theory".
- Potential_theory label "Potentialtheorie".
- Potential_theory label "Teoria del potenziale".
- Potential_theory label "Teoria do potencial".
- Potential_theory label "Teoria potencjału".
- Potential_theory label "Teoría del potencial".
- Potential_theory label "Théorie du potentiel".
- Potential_theory label "Теория потенциала".
- Potential_theory label "位势论".
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- Potential_theory sameAs m.050_js.
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- Potential_theory sameAs Q1154848.
- Potential_theory sameAs Q1154848.
- Potential_theory sameAs Potential_theory.
- Potential_theory wasDerivedFrom Potential_theory?oldid=603138322.
- Potential_theory isPrimaryTopicOf Potential_theory.