Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Potential_theory> ?p ?o }
- 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 wikiPageLength "9436".
- Potential_theory wikiPageOutDegree "61".
- Potential_theory wikiPageRevisionID "683296030".
- Potential_theory wikiPageWikiLink Analytic_function.
- Potential_theory wikiPageWikiLink Banach_space.
- Potential_theory wikiPageWikiLink Bergman_space.
- Potential_theory wikiPageWikiLink Bloch_space.
- Potential_theory wikiPageWikiLink Bxc3xb4chers_theorem.
- Potential_theory wikiPageWikiLink Casorati–Weierstrass_theorem.
- Potential_theory wikiPageWikiLink Category:Mathematical_physics.
- Potential_theory wikiPageWikiLink Category:Partial_differential_equations.
- Potential_theory wikiPageWikiLink Category:Potential_theory.
- Potential_theory wikiPageWikiLink Complex_number.
- Potential_theory wikiPageWikiLink Conformal_group.
- Potential_theory wikiPageWikiLink Conformal_map.
- Potential_theory wikiPageWikiLink Discrete_set.
- Potential_theory wikiPageWikiLink Disk_(mathematics).
- Potential_theory wikiPageWikiLink Domain_(mathematics).
- Potential_theory wikiPageWikiLink Domain_of_a_function.
- Potential_theory wikiPageWikiLink Electrical_network.
- Potential_theory wikiPageWikiLink Electrostatics.
- Potential_theory wikiPageWikiLink Essential_singularity.
- Potential_theory wikiPageWikiLink Euclidean_space.
- Potential_theory wikiPageWikiLink Force.
- Potential_theory wikiPageWikiLink Fourier_series.
- Potential_theory wikiPageWikiLink Hardy_space.
- Potential_theory wikiPageWikiLink Harmonic_function.
- Potential_theory wikiPageWikiLink Harmonic_functions.
- Potential_theory wikiPageWikiLink Harnacks_inequality.
- Potential_theory wikiPageWikiLink Harnacks_principle.
- Potential_theory wikiPageWikiLink Harnacks_theorem.
- Potential_theory wikiPageWikiLink Hilbert_space.
- Potential_theory wikiPageWikiLink Inner_product.
- Potential_theory wikiPageWikiLink Inner_product_space.
- Potential_theory wikiPageWikiLink Isolated_point.
- Potential_theory wikiPageWikiLink Isolated_singularity.
- Potential_theory wikiPageWikiLink Joseph_L._Doob.
- Potential_theory wikiPageWikiLink Kelloggs_theorem.
- Potential_theory wikiPageWikiLink Kelvin_transform.
- Potential_theory wikiPageWikiLink Laplaces_equation.
- Potential_theory wikiPageWikiLink Laurent_series.
- Potential_theory wikiPageWikiLink Level_set.
- Potential_theory wikiPageWikiLink Limit_of_a_sequence.
- Potential_theory wikiPageWikiLink Linear_map.
- Potential_theory wikiPageWikiLink Linear_transformation.
- Potential_theory wikiPageWikiLink Markov_chain.
- Potential_theory wikiPageWikiLink Mathematical_physics.
- Potential_theory wikiPageWikiLink Mathematical_singularity.
- Potential_theory wikiPageWikiLink Mathematics.
- Potential_theory wikiPageWikiLink Maximum_principle.
- Potential_theory wikiPageWikiLink Method_of_images.
- Potential_theory wikiPageWikiLink Moreras_theorem.
- Potential_theory wikiPageWikiLink Newtonian_gravity.
- Potential_theory wikiPageWikiLink Newtons_law_of_universal_gravitation.
- Potential_theory wikiPageWikiLink Normed_vector_space.
- Potential_theory wikiPageWikiLink Oliver_Dimon_Kellogg.
- Potential_theory wikiPageWikiLink Orbifold.
- Potential_theory wikiPageWikiLink Physics.
- Potential_theory wikiPageWikiLink Pole_(complex_analysis).
- Potential_theory wikiPageWikiLink Removable_singularity.
- Potential_theory wikiPageWikiLink Riemannian_manifold.
- Potential_theory wikiPageWikiLink Schwarz_lemma.
- Potential_theory wikiPageWikiLink Sheldon_Axler.
- Potential_theory wikiPageWikiLink Singularity_(mathematics).
- Potential_theory wikiPageWikiLink Sphere.
- Potential_theory wikiPageWikiLink Spherical_harmonic.
- Potential_theory wikiPageWikiLink Spherical_harmonics.
- Potential_theory wikiPageWikiLink Subgroup.
- Potential_theory wikiPageWikiLink Subharmonic_function.
- Potential_theory wikiPageWikiLink Symmetry.
- Potential_theory wikiPageWikiLink Vector_space.
- Potential_theory wikiPageWikiLink Weierstrass-Casorati_theorem.
- Potential_theory wikiPageWikiLinkText "Liouville's theorem".
- Potential_theory wikiPageWikiLinkText "Potential theory".
- Potential_theory wikiPageWikiLinkText "potential function".
- Potential_theory wikiPageWikiLinkText "potential functions".
- Potential_theory wikiPageWikiLinkText "potential theory".
- Potential_theory wikiPageWikiLinkText "potential".
- Potential_theory wikiPageWikiLinkText "potentials method".
- Potential_theory wikiPageWikiLinkText "theory of potential".
- Potential_theory wikiPageWikiLinkText "theory of potentials".
- 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 "potentialtheory".
- Potential_theory wikiPageUsesTemplate Template:Cite_arXiv.
- Potential_theory wikiPageUsesTemplate Template:Dubious.
- Potential_theory wikiPageUsesTemplate Template:PlanetMath_attribution.
- Potential_theory wikiPageUsesTemplate Template:Refbegin.
- Potential_theory wikiPageUsesTemplate Template:Refend.
- Potential_theory wikiPageUsesTemplate Template:Springer.
- Potential_theory subject Category:Mathematical_physics.
- Potential_theory subject Category:Partial_differential_equations.