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Erschienen in:
2009 | OriginalPaper | Buchkapitel
On Elliptic Operators in Nondivergence and in Double Divergence Form
verfasst von : Robert McOwen
Erschienen in: Analysis, Partial Differential Equations and Applications
Verlag: Birkhäuser Basel
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This work surveys results on the existence and asymptotic behavior of the fundamental solution for an elliptic operator
L
in nondivergence form, including recent results for operators whose coefficients are continuous with mild conditions on the modulus of continuity: if the square of the modulus of continuity satisfies the Dini condition, then there is an integral invariant which controls the behavior of solutions of
L
*
u
=0 and whether there is a fundamental solution for
L
that is asymptotic to the fundamental solution for the associated constant coefficient operator.