We consider a problem of mixed Cauchy type for certain holomorphic partialdifferential operators whose principal part $Q_{2p}(D)$ essentially is the(complex) Laplace operator to a power, $\Delta^p$. We pose inital data on asingular conic divisor given by P=0, where $P$ is a homogeneous polynomial ofdegree $2p$. We show that this problem is uniquely solvable if the polynomial$P$ is elliptic, in a certain sense, with respect to the principal part$Q_{2p}(D)$.
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机译：我们考虑某些全纯偏微分算子的混合柯西类型问题，这些算子的主要部分$ Q_ {2p}（D）$本质上是幂\\ Delta ^ p $的（复杂）拉普拉斯算子。我们将初始数据放在由P = 0给出的奇异圆锥除数上，其中$ P $是度$ 2p $的齐次多项式。我们证明，如果多项式$ P $在某种意义上相对于主体部分$ Q_ {2p}（D）$是椭圆的，则此问题是唯一可解决的。
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