Principal fundamental solution
A fundamental solution , defined throughout the space , of a second-order elliptic equation
that satisfies the conditions
for certain positive constants and if .
If the coefficients , and satisfy a Hölder condition on and if the inequality is satisfied for some , then a principal fundamental solution exists. If the coefficients of the operator are defined in a certain bounded domain with smooth boundary, then they can be extended to the entire space so that a principal fundamental solution will exist for the extended operator.
|||C. Miranda, "Partial differential equations of elliptic type" , Springer (1970) (Translated from Italian)|
Principal fundamental solution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_fundamental_solution&oldid=14964