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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( b ) Let u ( x1 , ... , , xn ) be continuous and bounded in the half - space xn > 0 , and be harmonic for xn > 0 and vanish for xin 0. Show that u = 0.
Associating with a functional o , ( that does not vanish identically ) , the hyperplane a in H consisting of the points u with $ ( u ) = 1 , we can think of ...
... solution of the wave equation with initial values 0 , thus vanish identically . ... with initial values that are 0 everywhere , and hence would vanish .
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