holds true for all functions (smooth functions with compact support in ) and for all . Notice that the integrals involved are well defined since is bounded with compact support and because is assumed to be integrable on compact subsets of .
The weak derivative is unique (as an element of the Lebesgue space ) in view of a result about locally integrable functions.
The same definition can be given for functions with complex values.
|Date of creation||2013-03-22 14:54:52|
|Last modified on||2013-03-22 14:54:52|
|Last modified by||paolini (1187)|