Cauchy's Problem for Hyperbolic Equations |
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Cauchy's Problem for Hyperbolic Equations: Winter and Spring Quarters, 1957 ... Lars Garding,G. Bergendahl No preview available - 2013 |
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ak+1 assumptions Banach space bounded coefficients bounded variation Cauchy's problem characteristic polynomial Consider continuous functions converges D₁ D₁h D₂ D₂h defined denoted derivatives of order double differential operator double order dual dual space duality equivalence Ɛ Lip¹ f Ɛ fact finite following lemma formula Friedrichs function f Hahn-Banach theorem Helly's theorem Hence hermitian Hölder's inequality homogeneous hyperbolic equations hyperbolic operators implies infinitely differentiable integrable functions left side lemma Leray let f linear functional linear homeomorphism Lipps locally integrable locally integrable function norm normal notation operator of order Pa(x Pak+1 partial adjoints prove the lemma remains to prove Remark replaced respectively result right side satisfying second kind sense tends to zero term theorem 7.1 unique solution vanishing in neighborhoods variable weakly dense write z)dz дево