Publication: On Approximation of Linear Second Order Elliptic Partial Differential Equations with Analytic Coefficients
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Date
2007
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
EUT Edizioni Università di Trieste
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.
Description
Keywords
Elliptic Partial Differential Equations, Bergman and Gilbert Integral Operator, Order and Type, Approximation Error
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.