Author | Wermer, John. author |
---|---|

Title | Potential Theory [electronic resource] / by John Wermer |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1974 |

Connect to | http://dx.doi.org/10.1007/978-3-662-12727-8 |

Descript | VIII, 149 p. 22 illus. online resource |

SUMMARY

Potential theory grew out of mathematical physics, in particular out of the theory of gravitation and the theory of electrostatics. Mathematical physicists such as Poisson and Green introduced some of the central ideas of the subject. A mathematician with a general knowledge of analysis may find it useful to begin his study of classical potential theory by looking at its physical origins. Sections 2, 5 and 6 of these Notes give in part heuristic arguments based on physical considerations. These heuristic arguments suggest mathematical theorems and provide the mathematician with the problem of finding the proper hypotheses and mathematical proofs. These Notes are based on a one-semester course given by the author at Brown University in 1971. On the part of the reader, they assume a knowledge of Real Function Theory to the extent of a first year graduate course. In addition some elementary facts regarding harmonic functions are aS$umed as known. For convenience we have listed these facts in the Appendix. Some notation is also explained there. Essentially all the proofs we give in the Notes are for Euclidean 3-space R3 and Newtonian potentials ̃

CONTENT

2. Electrostatics -- 3. Poissonโ{128}{153}s Equation -- 4. Fundamental Solutions -- 5. Capacity -- 6. Energy -- 7. Existence of the Equilibrium Potential -- 8. Maximum Principle for Potentials -- 9. Uniqueness of the Equilibrium Potential -- 10. The Cone Condition -- 11. Singularities of Bounded Harmonic Functions -- 12. Greenโ{128}{153}s Function -- 13. The Kelvin Transform -- 14. Perronโ{128}{153}s Method -- 15. Barriers -- 16. Kelloggโ{128}{153}s Theorem -- 17. The Riesz Decomposition Theorem -- 18. Applications of the Riesz Decomposition -- 19. Appendix -- 20. References -- 21. Bibliography -- 22. Index

Mathematics
Potential theory (Mathematics)
Mathematics
Potential Theory