A remark on the uniqueness for backward parabolic operators with non-Lipschitz-continuous coefficients. (English) Zbl 1258.35004

Ruzhansky, Michael (ed.) et al., Evolution equations of hyperbolic and Schrödinger type. Asymptotics, estimates and nonlinearities. Based on a workshop on asymptotic properties of solutions to hyperbolic equations, London, UK, March 2011. Basel: Springer (ISBN 978-3-0348-0453-0/hbk; 978-3-0348-0454-7/ebook). Progress in Mathematics 301, 103-114 (2012).
Summary: Using Bony’s paramultiplication we improve a result obtained in [the author and M. Prizzi, J. Math. Pures Appl., IX. Sér. 84, No. 4, 471–491 (2005; Zbl 1074.35042)] for operators having coefficients non-Lipschitz-continuous with respect to \(t\) but \(C^2\) with respect to \(x\), showing that the same result is valid when \(C^2\) is replaced by \( C^{1,\varepsilon}\), with \(\varepsilon > 0\).
For the entire collection see [Zbl 1250.35006].


35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35K15 Initial value problems for second-order parabolic equations


Zbl 1074.35042
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