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1
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Contact integrable extensions and differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation

100%
Morozov O.
Open Mathematics
|
2012
|
tom 10
|
nr 5
1688-1697
EN
The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
2
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Exponential coordinates and regularity of groupoid heat kernels

100%
So B.
Open Mathematics
|
2014
|
tom 12
|
nr 2
284-297
EN
We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.
3
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A recursion operator for the universal hierarchy equation via Cartan’s method of equivalence

84%
Morozov O.
Open Mathematics
|
2014
|
tom 12
|
nr 2
271-283
EN
We apply Cartan’s method of equivalence to find a Bäcklund autotransformation for the tangent covering of the universal hierarchy equation. The transformation provides a recursion operator for symmetries of this equation.
4
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Layer potentials C*-algebras of domains with conical points

68%
Carvalho C., Qiao Y.
Open Mathematics
|
2013
|
tom 11
|
nr 1
27-54
EN
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm conditions for the natural pseudodifferential operators affiliated to this C*-algebra.
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