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. |
Dentro del libro
Resultados 1-3 de 28
Página 65
... neighborhood N of y and positive numbers M , r such that for all xe N 1 – f ( x ) = Σ ; ( Daƒ ( y ) ) ( x − y ) a α a ! | D3fx ( x ) | ≤ M | B | ! r- | B | for all ẞe Z " and all k . ( 3.9a ) ( 3.9b ) Real analytic ƒ enjoy the ...
... neighborhood N of y and positive numbers M , r such that for all xe N 1 – f ( x ) = Σ ; ( Daƒ ( y ) ) ( x − y ) a α a ! | D3fx ( x ) | ≤ M | B | ! r- | B | for all ẞe Z " and all k . ( 3.9a ) ( 3.9b ) Real analytic ƒ enjoy the ...
Página 67
... neighborhood of the origin . We say f is majorised by F ( in symbols : f < F ) , if | Daƒ ( 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 f is majorised by F ( in symbols : f < F ) , if | Daƒ ( 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 έ 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 έ 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 |
Examples | 2 |
Analytic Solution and Approximation Methods in a Simple Example Problems 4 Quasilinear Equations | 4 |
Derechos de autor | |
Otras 35 secciones no mostradas
Otras ediciones - Ver todas
Términos y frases comunes
analytic functions assume ball boundary bounded uniformly Cauchy data Cauchy problem Cauchy sequence Chapter characteristic curves class C² coefficients compact support complex constant continuous converge defined denote derivatives of orders difference quotients Dirichlet problem domain of dependence elliptic exists follows formula Fourier function f fundamental solution Gårding Gårding's inequality given harmonic function heat equation hence Hint Ho(N holds identity implies inequality initial data initial values initial-value problem integral surface Laplace equation Lemma linear matrix maximum principle neighborhood non-characteristic norm obtained open set partial differential equation plane polynomial power series prescribed proof real analytic real numbers satisfies scalar Show solution u(x,t solved space square integrable sufficiently small test functions theorem u₁ vanish variables vector wave equation x₁ ΘΩ