Reduction of orders in boundary value problems without transmission property. (English) Zbl 1050.58019

Authors’ summary: Boundary value problems for elliptic pseudo-differential operators without the transmission property at the boundary appear in parametrices of mixed elliptic problems such as the Zaremba problem. The paper is devoted to the construction of order reductions in boundary value problems on a manifold with smooth boundary which play a crucial role in calculating the number of additional interface conditions. Moreover, the authors show that the order reducing symbols have the Volterra property and are parabolic of anisotropy 1. The results are then extended to order reducing holomorphic operator-valued Mellin symbols for reducing orders in weighted Sobolev spaces on a manifold with conical singularities on the boundary.


58J40 Pseudodifferential and Fourier integral operators on manifolds
35J40 Boundary value problems for higher-order elliptic equations
35S15 Boundary value problems for PDEs with pseudodifferential operators
35K25 Higher-order parabolic equations
58J32 Boundary value problems on manifolds
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