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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For a < 0 the solutions of ( 6.5 ) generally become singular at the origin . More precisely the only solution u of ( 6.5 ) of class C'in a neighborhood of ...
First of all , one transforms xo into the origin and S locally by an analytic transformation into a neighborhood of the origin in the plane X xn 0.
... with initial conditions u ( xj , ... , Xn - 1,0 ) = 0 for j = 1 , ... , N ( 3.38b ) where the G ; are real analytic at the origin in their arguments .
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