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Overdetermined Elliptic Systems
Foundations of Computational Mathematics, 2005We consider linear overdetermined systems of partial differential equations. We show that the introduction of weights classically used for the definition of ellipticity is not necessary, as any system that is elliptic with respect to some weights becomes elliptic without weights during its completion to involution.
Katsiaryna Krupchyk +2 more
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A Lyapunov Lemma for Elliptic Systems
Annals of Global Analysis and Geometry, 2004The authors of this very well written article prove an interesting result within the functional calculus of classical pseudo-differential operators. More precisely, they fix an \(N\times N\) system \(A\) of classical pseudo-differential operators of order \(\leq m\) on a compact smooth manifold and they assume that \(A\) is elliptic.
PARENTI, CESARE, PARMEGGIANI, ALBERTO
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Asymptotics for Semilinear Elliptic Systems
Canadian Mathematical Bulletin, 1991AbstractA class of weakly coupled systems of semilinear elliptic partial differential equations is considered in an exterior domain in ℝN, N > 3. Necessary and sufficient conditions are given for the existence of a positive solution (componentwise) with the asymptotic decay u(x) = O(|x|2-N) as |x| —> ∞.
Noussair, Ezzat S., Swanson, Charles A.
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Interface Problems for Elliptic Systems
Journal of Partial Differential Equations, 1999Summary: Interface problems for elliptic systems of second-order partial differential equations are studied. The main result is that the solution in the neighborhood of a singular point can be divided into two parts one of which is a solution to the homogeneous system with constant coefficients, and the other one possesses higher regularity.
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