TY - JOUR
T1 - A property of the β-Cauchy-type integral with continuous density
AU - Abreu Blaya, R.
AU - Bory Reyes, J.
N1 - Funding Information:
Partially supported by the CAPES-MES Project 028/07.
PY - 2008/11
Y1 - 2008/11
N2 - A theorem from the classical complex analysis proved by Davydov in 1949 is extended to the theory of solution of a special case of the Beltrami equation in the z-complex plane (i.e., null solutions of the differential operator equation is present. It is proved that if γ is a rectifiable Jordan closed curve and f is a continuous complex-valued function on γ such that the integral equation is present converges uniformly on γ as r∈→∈0, where n(ζ) is the unit vector of outer normal on γ at a point ζ and ds is the differential of arc length, then the β-Cauchy-type integral equation is present admits a continuous extension to γ and a version of the Sokhotski-Plemelj formulas holds.
AB - A theorem from the classical complex analysis proved by Davydov in 1949 is extended to the theory of solution of a special case of the Beltrami equation in the z-complex plane (i.e., null solutions of the differential operator equation is present. It is proved that if γ is a rectifiable Jordan closed curve and f is a continuous complex-valued function on γ such that the integral equation is present converges uniformly on γ as r∈→∈0, where n(ζ) is the unit vector of outer normal on γ at a point ζ and ds is the differential of arc length, then the β-Cauchy-type integral equation is present admits a continuous extension to γ and a version of the Sokhotski-Plemelj formulas holds.
UR - http://www.scopus.com/inward/record.url?scp=67349117329&partnerID=8YFLogxK
U2 - 10.1007/s11253-009-0162-8
DO - 10.1007/s11253-009-0162-8
M3 - Artículo
SN - 0041-5995
VL - 60
SP - 1683
EP - 1690
JO - Ukrainian Mathematical Journal
JF - Ukrainian Mathematical Journal
IS - 11
ER -