Abstract
The purpose of the research is to assign a formally exact elliptic complex of length two to the Cauchy-Riemann Operator. The Neumann problem for this complex in a bounded domain with smooth boundary in R2 will be studied, helping therefore to solve a usual boundary value problem for the Cauchy-Riemann operator.
Highlights
Open AccessMost first order linear differential operators of geometric origin are Dirac operators
Dirac operators on Riemannian manifolds are of fundamental importance in differential geometry
We denote by σ 1 ( D)(ξ ) the principal symbol of D. The rank of this matrix is equal to k for all ξ ∈ n \ {0}. It follows that every Dirac type operator is overdetermined elliptic
Summary
Most first order linear differential operators of geometric origin are Dirac operators. The rank of this matrix is equal to k for all ξ ∈ n \ {0} It follows that every Dirac type operator is overdetermined elliptic. We firstly restrict our discussion to a boundary value problem related to the Cauchy-Riemann operator, which is a Dirac type operator. The scheme of the article can be declined in the following way: In Section 2, we show that boundary value problem related to the Cauchy-Riemann operator in the plane satisfies the Lopatinskii condition. To this end, finding a compatible complex to.
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