Partial Differential Equations
Springer, 1982 - 249 páginas
This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy 's example of a linear equation without solutions.
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More generally , we are led to the notion of a distribution . Definition . A distribution is a linear functional f [ 0 ] defined for all QE D = CO ° ( 12 ) ...
For a distribution f we define the “ derivative ” Dkf as the distribution given by Dxf [ ° ] = - f ... ( 6.13 ) actually define distributions Duf , Daf .
Then u ( x ) = | x- $ | is a fundamental solution for L. Indeed the distribution associated with u " by ( 6.13 ) is + oo u " [ 0 ] = u [ ^ " ] = S4 | x – fl ...
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