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 49
... norm " : || v || = sup sup k = 1 , ... , N x ; 0 < t < T | vx ( x , t ) | . ( 5.25 ) The norm || S || of the operator S ( the supremum of || Sv || for || v || = 1 ) obviously is bounded * by the constant q = 7 sup Σck ( x , t ) | . i ...
... norm " : || v || = sup sup k = 1 , ... , N x ; 0 < t < T | vx ( x , t ) | . ( 5.25 ) The norm || S || of the operator S ( the supremum of || Sv || for || v || = 1 ) obviously is bounded * by the constant q = 7 sup Σck ( x , t ) | . i ...
Página 167
... norm |||||| also are Cauchy sequences with respect to the norm || v || , it follows that ( A ̄1v , w ) defines a bounded linear functional on H. By the representation theorem ( p . 118 ) we can then find an element U in H such that ( A ...
... norm |||||| also are Cauchy sequences with respect to the norm || v || , it follows that ( A ̄1v , w ) defines a bounded linear functional on H. By the representation theorem ( p . 118 ) we can then find an element U in H such that ( A ...
Página 190
... norm ( 2.3 ) of the set of functions in C ( ) with bounded norm || u || ,. We can identify H ° ( N ) with H ° ( N ) or with the set L2 ( N ) of u that are square integrable over N in the sense of Lebesgue . For " nice " and " nice " u ...
... norm ( 2.3 ) of the set of functions in C ( ) with bounded norm || u || ,. We can identify H ° ( N ) with H ° ( N ) or with the set L2 ( N ) of u that are square integrable over N in the sense of Lebesgue . For " nice " and " nice " u ...
Contenido
Chapter | 1 |
Examples | 2 |
Analytic Solution and Approximation Methods in a Simple Example Problems 4 Quasilinear Equations | 4 |
Derechos de autor | |
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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