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Prescribing Gevrey singularities for solutions of pseudodifferential operators. (English) Zbl 1196.35238

The authors obtain conditions by means of a priori estimates to ensure the existence of distribution or smooth solutions with prescribed Gevrey wave front sets for pseudodifferential operators of finite order. To illustrate the results, a concrete example is analysed in detail.

MSC:

35S05 Pseudodifferential operators as generalizations of partial differential operators
35D30 Weak solutions to PDEs
35A18 Wave front sets in context of PDEs
35B45 A priori estimates in context of PDEs
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46F05 Topological linear spaces of test functions, distributions and ultradistributions
58J40 Pseudodifferential and Fourier integral operators on manifolds
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