Unique continuation for parabolic operators

By Luis Escauriaza, F. J. Fernández. 2003

116 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fb111620776a5ecbbcb85e1de5c8253ada86c070

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. D. Tataru
2. Herbert Koch
3. Carlos E. Kenig
4. Jonathan J. Zhu
5. G. Koch
6. Terence Tao
7. Lu Wang
8. Xin Zhou

In Computational Theory and Mathematics

1. Herbert Koch
2. D. Tataru
3. Lu Wang
4. Carlos E. Kenig
5. G. Koch
6. Luis Escauriaza
7. Agnid Banerjee
8. Jonathan J. Zhu

In Mathematical Physics

1. Carlos E. Kenig
2. D. Tataru
3. Herbert Koch
4. Terence Tao
5. G. Koch
6. Jonathan J. Zhu
7. Lu Wang
8. B. Dodson

Citations in the corpus

• Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations (2017, background): “can be thought of as the nonlocal counterpart of the monotonicity formula first proved by Poon in [Po] for the local case s= 1. In connection with the local case we also refer to the interesting works [EF], [EFV], where a space-like unique continuation property for local solutions has been establishe”
• Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients (2007, background): “Fernández [11], and Escauriaza, Fernández and Vessella [7] considered SUCP(II) under various assumptions on the coefficients and pointwise bounds for W = 0 and V .”
• Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends (2011, methodology): “4Under slightly different notations, a similar identity might have already been implicitly obtained in [13].”
• Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, unknown): “However, since the elliptic operators in our problem are actually Laplacians relative to g(τ) (and so also perturbations of a conical Laplacian), our situation is fundamentally simpler than that of [29], and we find that the approach of [30] yields estimates with somewhat more transparent geometric ”
• An alternative approach to regularity for the Navier–Stokes equations in critical spaces (2009, background): “nd the following “unique continuation” theorem, a proof of which can be found in [14] but which was already a well-known fact from the unique continuation theory of differential inequalities (see also [15]): Theorem 3.11 (Unique Continuation). Let Qr,δ := Br(0) × (−δ,0) for some r,δ > 0, and suppo”
• Observability Inequalities and Measurable Sets (2012, background): “We begin with the following Carleman inequality (See [9] and [11]).”
• Existence of hypersurfaces with prescribed mean curvature I – generic min-max (2018, background): “eflowissmooth on [0,t0], we have |A|2 + |Ric(ν,ν)| ≤ C<∞. The conclusion follows from the spacelike strong unique continuation principle for parabolic PDE (see for instance [60, Corollary 4.2.7] or [20, 2]) and backwards uniqueness for mean curvature flow [38, 40]. 3.4. Estimates for the touching s”