SMOOTHING EFFECTS OF DISPERSIVE PSEUDODIFFERENTIAL EQUATIONS
SMOOTHING EFFECTS OF DISPERSIVE PSEUDODIFFERENTIAL EQUATIONS
复制标题
色散伪微分方程的平滑效应
DOI：
10.1081/pde-120016133
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发表时间：
2002
影响因子：
1.9
通讯作者：
H. Chihara
中科院分区：
文献类型：
--
作者：
H. Chihara
摘要讨论了主部不一定是椭圆的色散型伪微分方程的光滑效应。对于常系数方程，利用限制定理和主部预解式的光滑估计，得到了加权Lebesgue空间中解的光滑估计。此外，我们还讨论了初值问题的适定性，并通过伪微分法给出了一般变系数色散方程光滑效应的另一种方法。我们的结果是薛定谔型方程光滑效应的自然推广。
ABSTRACT We discuss smoothing effects of dispersive-type pseudodifferential equations whose principal part is not necessarily elliptic. For equations with constant coefficients, a restriction theorem and a smoothing estimate of the resolvent of the principal part obtain smoothing estimates of solutions in weighted Lebesgue spaces. Moreover, we discuss well-posedness of the initial value problem and an alternative approach to the smoothing effects of general dispersive equations with variable coefficients via pseudodifferential calculus. Our results are the natural generalization of smoothing effects of Schrödinger-type equations.