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2002 On an estimate for the wave equation and applications to nonlinear problems
Sigmund Selberg
Differential Integral Equations 15(2): 213-236 (2002).


We prove estimates for solutions of the Cauchy problem for the inhomogeneous wave equation on $\mathbb R^{1+n}$ in a class of Banach spaces whose norms depend only on the size of the space--time Fourier transform. The estimates are local in time, and this allows one, essentially, to replace the symbol of the wave operator, which vanishes on the light cone in Fourier space, with an inhomogeneous symbol, which can be inverted. Our result improves earlier estimates of this type proved by Klainerman--Machedon [4, 5]. As a corollary, one obtains a rather general result concerning local well-posedness of nonlinear wave equations, which was used extensively in the recent article [8].


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Sigmund Selberg. "On an estimate for the wave equation and applications to nonlinear problems." Differential Integral Equations 15 (2) 213 - 236, 2002.


Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1032.35121
MathSciNet: MR1870470

Primary: 35L70
Secondary: 35B35

Rights: Copyright © 2002 Khayyam Publishing, Inc.


Vol.15 • No. 2 • 2002
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