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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We have to show that it has the prescribed boundary values f on as . This requires some additional assumption on the nature of the boundary as of 2.
The proof that v has boundary values 0 will be given here only for the dimension n = 2. ( For higher dimensions see p . 202. ) ...
... with boundary values f ( “ Dirichlet's principle ” ) . ... denote the boundary values assumed to be continuous , and u ( rcos , rsin ) the solution of ...
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