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 93
... sense of distributions . f ( x + h ) f ( x ) In ( x ) = = h Show that in the sense of distributions . lim f = Df h → 0 4 The Laplace Equation * 1. Green's Identity , Fundamental 6 Distribution Solutions 93.
... sense of distributions . f ( x + h ) f ( x ) In ( x ) = = h Show that in the sense of distributions . lim f = Df h → 0 4 The Laplace Equation * 1. Green's Identity , Fundamental 6 Distribution Solutions 93.
Página 121
... sense . Here the verification of the differential equation Av = w , say for wEC1 ( N ) , is not as difficult as to show that v = 0 on IN . One first observes that the solution v of the modified problem is represent- able by a Cauchy ...
... sense . Here the verification of the differential equation Av = w , say for wEC1 ( N ) , is not as difficult as to show that v = 0 on IN . One first observes that the solution v of the modified problem is represent- able by a Cauchy ...
Página 199
... sense of p . 90 . 2. Show that two elements u , v of Ho ( N ) are identical if the corresponding distributions are identical . 3. Show that the Dirac " function " is a distribution that is not generated by any u Є Ho ( N ) . 4. A ...
... sense of p . 90 . 2. Show that two elements u , v of Ho ( N ) are identical if the corresponding distributions are identical . 3. Show that the Dirac " function " is a distribution that is not generated by any u Є Ho ( N ) . 4. A ...
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