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 65
... neighborhood N of y and positive numbers M , r such that for all x E N 1 f ( x ) = Σ Σ ~ ( Daf ( y ) ) ( x − y ) a ( D * f ( y ) ) ( x – y ) a ! α \ D®ƒx ( x ) | ≤ M | B | ! r - 1B for all ẞ € Z " ( 3.9a ) and all k . ( 3.9b ) Real ...
... neighborhood N of y and positive numbers M , r such that for all x E N 1 f ( x ) = Σ Σ ~ ( Daf ( y ) ) ( x − y ) a ( D * f ( y ) ) ( x – y ) a ! α \ D®ƒx ( x ) | ≤ M | B | ! r - 1B for all ẞ € Z " ( 3.9a ) and all k . ( 3.9b ) Real ...
Página 67
... neighborhood of the origin . We say fis majorised by F ( in symbols : f < F ) , if \ Daƒx ( 0 ) | ≤ D ° F ( 0 ) for ... neighborhood of the origin of R " into Rm , and let g ( u ) , G ( u ) be C ° -maps of a neighborhood of the origin ...
... neighborhood of the origin . We say fis majorised by F ( in symbols : f < F ) , if \ Daƒx ( 0 ) | ≤ D ° F ( 0 ) for ... neighborhood of the origin of R " into Rm , and let g ( u ) , G ( u ) be C ° -maps of a neighborhood of the origin ...
Página 98
... neighborhood of a real point of . Formula ( 1.19 ) then defines u ( § ) as a differentiable function of in that complex neighborhood . It follows that u is real analytic in the set . We need not assume that uЄC2 ( M ) . To belong to C ...
... neighborhood of a real point of . Formula ( 1.19 ) then defines u ( § ) as a differentiable function of in that complex neighborhood . It follows that u is real analytic in the set . We need not assume that uЄC2 ( M ) . To belong to C ...
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