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- W73365714 abstract "Starting from first principles, all fundamental solutions (that are tempered distributions) for scalar elliptic operators are identified in this chapter. While the natural starting point is the Laplacian, this study encompasses a variety of related operators, such as the bi-Laplacian, the poly-harmonic operator, the Cauchy-Riemann operator, the Dirac operator, as well as general second order constant coefficient strongly elliptic operators. Having accomplished this task then makes it possible to prove the well-posedness of the Poisson problem (equipped with a boundary condition at infinity), and derive qualitative/quantitative properties for the solution. Along the way, Cauchy-like integral operators are also introduced and their connections with Hardy spaces is brought to light in the setting of both complex and Clifford analysis." @default.
- W73365714 created "2016-06-24" @default.
- W73365714 creator A5053496960 @default.
- W73365714 date "2013-01-01" @default.
- W73365714 modified "2023-09-27" @default.
- W73365714 title "The Laplacian and Related Operators" @default.
- W73365714 cites W4210551282 @default.
- W73365714 doi "https://doi.org/10.1007/978-1-4614-8208-6_7" @default.
- W73365714 hasPublicationYear "2013" @default.
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