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 EquationsBergman and Gilbert Integral OperatorOrder and TypeApproximation 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 Mathematics39 (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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