一类广义波方程的低正则性

The Minimal Regularity for a Class of Generalized Wave Equations

利用等价积分算子和Fourier变换的方法 ,研究高维空间中一类广义波方程utt-Δmu+p(x ,D)u=uk(x∈Rn,m、k∈Z+ ,k≥ 2 ,m ≥ 1,｜p(x ,ξ) ｜≤C｜ξ｜2m-1)的低正则性 ,得到了其Sobolev指数为 n2 - mk - 1.

In this paper, the minimal regularity for a class of generalized wave equations,u tt-Δ mu+p(x,D)u=u k(x∈R n,m,k∈Z +,k≥2,m≥1,|p(x,ξ)|≤C|ξ| 2m-1),in high space dimensions is studied by using equivalent integrable operator and Fourier transformation. It is proved that the Sobolev exponent is n2-mk-1.