论文标题
Strichartz对媒体中Maxwell方程的估计：完全各向异性的情况
Strichartz estimates for Maxwell equations in media: The fully anisotropic case
论文作者
论文摘要
我们证明了具有Hölder-Coninul系数的完全各向异性情况下的介质中Maxwell方程的Strichartz估计值。为此，我们使用FBI转换将问题结合到相位空间。通过矩阵对称器降低到标量估计值后，我们显示了可变的傅立叶扩展运算符的振荡积分估计值。特征表面具有任何非散布时间频率的圆锥形奇点。结合能量估计值，我们改善了某些完全各向异性的准线性麦克斯韦方程的局部良好性。
We prove Strichartz estimates for Maxwell equations in media in the fully anisotropic case with Hölder-continuous coefficients. To this end, we use the FBI transform to conjugate the problem to phase space. After reducing to a scalar estimate by means of a matrix symmetrizer, we show oscillatory integral estimates for a variable-coefficient Fourier extension operator. The characteristic surface has conical singularities for any non-vanishing time frequency. Combined with energy estimates, we improve the local well-posedness for certain fully anisotropic quasilinear Maxwell equations.
