The mixed Cauchy problem for holomorphic partial differential operators
This paper deals with linear partial differential equations with analytic coefficients and the problem of finding holomorphic solutions which take prescribed values on each of an appropriate number of irreducible analytic hypersurfaces. The analysis proposed in the paper is local. It is interesting to note that even local existence for the mixed Cauchy problem is not valid in general although existence results are proved in some particular situations. As it concerns uniqueness of solutions it depends only on the principal part of the operator and the tangent hyperplanes of the initial manifolds. The authors illustrate their assertions with new results for the Laplace operator.
scientific article; zbMATH DE number 807409
scientific article