Principal fundamental solution
From Encyclopedia of Mathematics
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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.
References
| [1] | C. Miranda, "Partial differential equations of elliptic type" , Springer (1970) (Translated from Italian) |
How to Cite This Entry:
Principal fundamental solution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_fundamental_solution&oldid=14964
Principal fundamental solution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_fundamental_solution&oldid=14964
This article was adapted from an original article by Sh.A. Alimov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article