对合重特征边值问题的奇性反射

设ΩＲ（ｎ＋１），其边界　Ω在ｘ０∈　Ω附近局部为｛ｔ＝０｝，且对ｍ阶偏微分算子Ｐ（ｘ，ｔ，Ｄｘ，Ｄｔ）是非特征的．令σｍ（Ｐ）（ｘ，ｔ，ζ，Ｔ）＝０关于Ｔ有ｍ个实根（包括重根）λｊ（ｘ，ｔ，ζ），（ｊ＝１，．．．，ｍ），且它们是对合组．在Ｐ（ｘ，ｔ，Ｄｘ，Ｄｔ）满足Ｌｅｖｉ条件下，则其Ｄｉｒｉｃｈｌｅｔ边值问题的解ｕ的Ｃ∞奇性在边界的反射锥族中是不变的．

Reflection of Singularities for Boundary Value Problem of Operators with Involutive Characteristics of Variable Multiplicity

Let Ω, the boundary on be locally {t = o} near x0∈ Ω,andΩ is non characteristics for m-order partial differential operator P(x, t, Dx, Dt).Suppose that there are m real roots (containing multiple roots)λj(x, t,ξ), (j =1,..., m) of the equation σ(P)(x, t, ξ,) = 0in and the involutive condition is satisfied. Then under the Levi condition we get that the C∞ singularity of solutions u of the Dirichlet boundary value problem for P is invaxiable in reflection conic class of the boundary.