Estimates for Solutions of Wave Equations with Vanishing Curvature
1985 ◽
Vol 37
(6)
◽
pp. 1176-1200
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Keyword(s):
The solution of the Cauchy problem for a hyperbolic partial differential equation leads to a linear combination of operators Tt of the formFor example, the solution of the initial value problemis given by u(x, t) = Ttf(x) wherePeral proved in [11] that Tt is bounded from LP(Rn) to LP(Rn) if and only ifFrom the homogeneity, the operator norm satisfies ‖Tt‖ ≦ Ct for all t > 0.
1959 ◽
Vol 3
(1)
◽
pp. 355-380
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1980 ◽
Vol 3
(1)
◽
pp. 103-111
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1979 ◽
Vol 71
(1)
◽
pp. 167-186
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1990 ◽
Vol 427
(1872)
◽
pp. 221-239
◽
2014 ◽
Vol 144
(6)
◽
pp. 1191-1244
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