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Lp-Lq DECAY ESTIMATES FOR HYPERBOLIC EQUATIONS WITH OSCILLATIONS IN COEFFICIENTS |
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| Authors: | M. REISSIG K. YAGDJIAN |
| Affiliation: | 1. Faculty of Mathematics and Computer Science,Freiberg University of Mining and Technology, Bernhard yon Cotta Str. 2, D-09596 Freiberg, Germany 2. Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan |
| Abstract: | This work is concerned with the proof ofL p -L q decay estimates for solutions of the Cauchy problem foru tt −λ2(t)b 2(t)Δu=0. The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded functionb which are uniformly separated from zero. The authors' main interest is devoted to the critical case where one has an interesting interplay between the growing and the oscillating part. |
| Keywords: | L p -L q decay estimates Wave equation Fourier multipliers |
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