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Applications that Depend on Conformal Mapping

In: Handbook of Complex Variables

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  • Steven G. Krantz

    (Washington University in St. Louis, Department of Mathematics)

Abstract

Part of the utility of conformal mappings is that they can be used to transform a problem on a given domain V to another domain U (see also §§6.1.1). Often we take U to be a standard domain such as the disc 14.1.1.1 $$D = \{ z \in \mathbb{C}:|z| 0\} .$$ Particularly in the study of partial differential equations, it is important to have an explicit conformal mapping between the two domains. In the Appendix to this chapter we give a compendium of conformal mappings of some of the most frequently encountered planar regions.

Suggested Citation

  • Steven G. Krantz, 1999. "Applications that Depend on Conformal Mapping," Springer Books, in: Handbook of Complex Variables, chapter 0, pages 163-194, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1588-2_14
    DOI: 10.1007/978-1-4612-1588-2_14
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