Partial Differential EquationsSpringer, 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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Página 72
... corresponding to points y1 , ... , y contains S. Then the various functions F ( x ) corresponding to y = y1 , .. y1 , ... , y , ( denoted by F1 , convex sets ‚ F " ) uniquely define an analytic function F ( x ) in the set U. For if the ...
... corresponding to points y1 , ... , y contains S. Then the various functions F ( x ) corresponding to y = y1 , .. y1 , ... , y , ( denoted by F1 , convex sets ‚ F " ) uniquely define an analytic function F ( x ) in the set U. For if the ...
Página 140
... corresponding to the eigenvalue A is a solution of Av ( x ) + λv ( x ) = 0 for x EN v ( x ) = 0 for x E IN , ( 1.62a ) ( 1.62b ) where v does not vanish identically . Under appropriate regularity assump- tions on there exists a sequence ...
... corresponding to the eigenvalue A is a solution of Av ( x ) + λv ( x ) = 0 for x EN v ( x ) = 0 for x E IN , ( 1.62a ) ( 1.62b ) where v does not vanish identically . Under appropriate regularity assump- tions on there exists a sequence ...
Página 229
... corresponding to the choices h = 2 " , k = λ2-2 for v = 1,2 , .... Denote by v❞ the solution of ( 2.5a , b ) corresponding to Σ ,. If U is the union of all Σ , and ( x , t ) a point of U , then v ' ( x , t ) is well defined for all ...
... corresponding to the choices h = 2 " , k = λ2-2 for v = 1,2 , .... Denote by v❞ the solution of ( 2.5a , b ) corresponding to Σ ,. If U is the union of all Σ , and ( x , t ) a point of U , then v ' ( x , t ) is well defined for all ...
Contenido
Chapter | 1 |
Quasilinear Equations | 9 |
The Cauchy Problem | 24 |
Derechos de autor | |
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Términos y frases comunes
assume ball boundary bounded uniformly Cauchy data Cauchy problem Cauchy sequence Cauchy-Kowalevski Chapter characteristic curves class C² coefficients compact support complex constant continuous converge defined denote derivatives of orders determined uniquely difference quotients Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f(x fundamental solution Gårding given Green's identity heat equation hence Hint holds identity implies inequality initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix neighborhood non-characteristic norm obtained open set partial differential equation plane polynomial power series prescribed proof quasi-linear real numbers satisfies scalar second derivatives Show solved space square integrable sufficiently small test functions theorem u₁ vanish variables vector wave equation x₁ ΘΩ