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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4119

Title: On Approximation of Linear Second Order Elliptic Partial Differential Equations with Analytic Coefficients
Authors: Kumar, Devendra
Keywords: Elliptic Partial Differential Equations
Bergman and Gilbert Integral Operator
Order and Type
Approximation Error
Issue Date: 2007
Publisher: EUT Edizioni Università di Trieste
Citation: Devendra Kumar, "On Approximation of Linear Second Order Elliptic Partial Differential Equations with Analytic Coefficients”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 39 (2007), pp. 359–373.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (2007)
Abstract: The linear second-order elliptic differential equation with real-valued coefficients that are entire functions on $\Im^2$ and whose coefficient $c(x, y) \leq 0$ on the disk $D : x^2+y^2\leq1$ is given by $\Delta^2 v+a(x,y)v_x + b(x,y)v_y+c(x,y)v=0, (x,y)\in E^2$. The ideas of Bernstein and Saff have been applied by McCoy [9, 10] to study the singularities of certain second-order elliptic equations with singular coefficients. These results contain calculations of order and type of entire function potentials in terms of best polynomial approximation errors. Here some inequalities concerning order and type for the given equation have been obtained.
URI: http://hdl.handle.net/10077/4119
ISSN: 0049-4704
MS Classification: 30E10
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.39 (2007)

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