# On splitting up singularities of fundamental solutions to elliptic equations in ℂ2

Open Mathematics (2007)

- Volume: 5, Issue: 4, page 733-740
- ISSN: 2391-5455

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topT. Savina. "On splitting up singularities of fundamental solutions to elliptic equations in ℂ2." Open Mathematics 5.4 (2007): 733-740. <http://eudml.org/doc/269735>.

@article{T2007,

abstract = {It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.},

author = {T. Savina},

journal = {Open Mathematics},

keywords = {Complex Variables; Elliptic Equations; Fundamental Solution; complex variables; elliptic equations; fundamental solution; analytic coefficients; singularities on characteristics},

language = {eng},

number = {4},

pages = {733-740},

title = {On splitting up singularities of fundamental solutions to elliptic equations in ℂ2},

url = {http://eudml.org/doc/269735},

volume = {5},

year = {2007},

}

TY - JOUR

AU - T. Savina

TI - On splitting up singularities of fundamental solutions to elliptic equations in ℂ2

JO - Open Mathematics

PY - 2007

VL - 5

IS - 4

SP - 733

EP - 740

AB - It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.

LA - eng

KW - Complex Variables; Elliptic Equations; Fundamental Solution; complex variables; elliptic equations; fundamental solution; analytic coefficients; singularities on characteristics

UR - http://eudml.org/doc/269735

ER -

## References

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- [6] T.V. Savina: “On a reflection formula for higher-order elliptic equations/rd, Math. Notes, Vol. 57, no. 5–6, (1995), pp. 511–521. http://dx.doi.org/10.1007/BF02304421
- [7] T.V. Savina: “A reflection formula for the Helmholtz equation with the Neumann Condition/rd, Comput. Math. Math. Phys., Vol. 39, no. 4, (1999), pp. 652–660. Zbl0965.35028
- [8] T.V. Savina, B.Yu. Sternin and V.E. Shatalov: “On a reflection formula for the Helmholtz equation”, Radiotechnika i Electronica, (1993), pp. 229–240.
- [9] B.Yu. Sternin and V.E. Shatalov: Differential equations on complex manifolds, Mathematics and its Applications, Vol. 276, Kluwer Academic Publishers Group, Dordrecht, 1994. Zbl0818.35003
- [10] I.N. Vekua: New methods for solving elliptic equations, North Holland, 1967.
- [11] I.N. Vekua: Generalized analytic functions, Second edition, Nauka, Moscow, 1988.

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