- Sources
In the mathematical field of potential theory, Boggio's formula is an explicit formula for the Green's function for the polyharmonic Dirichlet problem on the ball of radius 1. It was discovered by the Italian mathematician Tommaso Boggio.
The polyharmonic problem is to find a function u satisfying
where m is a positive integer, and 
represents the Laplace operator. The Green's function is a function satisfying
where 
represents the Dirac delta distribution, and in addition is equal to 0 up to order m-1 at the boundary.
Boggio found that the Green's function on the ball in n spatial dimensions is
The constant 
is given by
where
Sources
- {{Citation|last=Boggio|first=Tomas|date=1905|title=Sulle funzioni di Green d'ordine m|periodical=Rendiconti del Circolo Matematico di Palermo|volume=20|pages=97–135|doi=10.1007/BF03014033}}
- {{Citation
| last1=Gazzola
| first1=Filippo
| author1-link=
| last2=Grunau
| first2=Hans-Christoph
| author2-link=
| last3=Sweers
| first3=Guido
| title=Polyharmonic Boundary Value Problems
| series=Lecture Notes in Mathematics
| volume=1991
| edition=
| publisher=Springer
| date=2010
| place=Berlin
| url=http://www1.mate.polimi.it/~gazzola/book_GGS.pdf
| isbn=978-3-642-12244-6
}}
2 : Elliptic partial differential equations|Potential theory
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