半线性波动方程的Sobolev指数

THE SOBOLEV EXPONENT FOR SEMILINEAR WAVE EQUATIONS

本文讨论半线性波动方程的Ｓｏｂｏｌｅｖ指数，与Ｐｏｎｃｅ和Ｓｉｄｅｒｉｓ（１９９３）得到的最新结果比较，本文得到的Ｓｏｂｏｌｅｖ指数更小型化了．

This paper deals with the Sobolev exponent for a semilinear wave equation u tt -Δu=u k( D u) α (k∈Z +,x∈R 3,|α|≥2), and obtains the Sobolev exporent s 0=2.  This result is better than that of Ponce and Sideris(1993).