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

• Autorzy: T. Savina
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Complex Variables; Elliptic Equations; Fundamental Solution

Kategorie tematyczne

• 32W50: Other partial differential equations of complex analysis
• 35J15: Second-order elliptic equations
• 32S70: Other operations on singularities

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 4
• Strony: 733-740

Daty

wydano

2007-12-01

online

2007-12-01

Twórcy

autor

T. Savina

• Ohio University

Bibliografia

• [1] D. Colton and R.P. Gilbert: “Singularities of solutions to elliptic partial differential equations with analytic coefficients”, Quart. J. Math. Oxford Ser. 2, Vol. 19, (1968), pp. 391–396. http://dx.doi.org/10.1093/qmath/19.1.391
• [2] F. John: “The fundamental solution of linear elliptic differential equations with analytic Coefficients”, Comm. Pure Appl. Math., Vol. 3, (1950), pp. 273–304. http://dx.doi.org/10.1002/cpa.3160030305
• [3] F. John: Plane waves and spherical means applied to partial differential equations, Springer-Verlag, New York-Berlin, 1981.
• [4] D. Khavinson: Holomorphic partial differential equations and classical potential theory, Universidad de La Laguna, 1996.
• [5] D. Ludwig: “Exact and Asymptotic solutions of the Cauchy problem/rd, Comm. Pure Appl. Math., Vol. 13, (1960), pp. 473–508. http://dx.doi.org/10.1002/cpa.3160130310
• [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.
• [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.
• [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.

Identyfikatory

DOI

10.2478/s11533-007-0027-z