【摘要】 考虑下列带有摄动位势波动方程解的Ｌｐ估计ｔｕ－Δｕ＋Ｖ（ｘ）ｕ＝０，ｕ（ｘ，０）＝０，ｔｕ（ｘ，０）＝ｆ（ｘ），｛（ｘ∈Ｒｎ，ｎ≥３）其中ｆ（ｘ）∈Ｌｐ（Ｒｎ），｜１ｐ－１２｜≤１ｎ－１．如果Ｖ（ｘ）是紧支集的小势，本文证明了以上问题的解和非摄动问题（Ｖ（ｘ）≡０）的解具有同样的Ｌｐ估计：ｕ（ｔ，）Ｐ≤Ｃｔｆｐ，ｔ＞０．更多还原

【Abstract】 We consider L pestimate for the following wave equation with a perturbed potential tt u-Δu+V(x)u=0, u(x,0)=0, tu(x,0)=f(x), (x∈R n,n≥3)where f(x)∈L p(R n),|1p-12|≤1n-1.If V(x) is a compact and small potential, then we prove that the solution of above problem has same  L pestimate as that of non perturbed problem (V(x)≡0),‖u(t,·)‖ p≤Ct‖f‖ p, t>0.更多还原