Elliptic partial differential equation

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Weyl transforms and a degenerate elliptic partial differential equation

Proceedings of the Royal Society A, 2005
M. W. Wong
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Stable Solutions of Elliptic Partial Differential Equations

2011
Defining Stability Stability and the variations of energy Linearized stability Elementary properties of stable solutions Dynamical stability Stability outside a compact set Resolving an ambiguity The Gelfand Problem Motivation Dimension N = 1 Dimension N = 2 Dimension N => 3 Summary Extremal Solutions Weak solutions Stable weak solutions The stable ...
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Recapturing Solutions of an Elliptic Partial Differential Equation

1981
Let k 2 -C(x 2 +y 2 )≤ 0 be regular on the closure of the disk D: x 2 +y 2 2 +(k 2 - C(x 2 +y 2 )}ϕ = 0. When the restriction of ϕ to the 3D is sufficiently smooth, expansion formulae are given that recapture ϕ from its means and shifted means on an arc of the 3D. A solution is given that interpolates prescribed means at the boundary.
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Numerical solution of elliptic partial differential equation using radial basis function neural networks