Backward Uniqueness for Parabolic Equations

By Luis Escauriaza, G A Seregin, Vladimír Sverák. 2003

233 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/93e613b61b49eddb1de92ec1f793f8df9a2cd636

How researchers see this paper

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

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

BACKWARD UNIQUENESS FOR THE HEAT OPERATOR IN A HALF-SPACE (2004, methodology): “As in [ 3 ] and [4], the proof of Theorem 1.1 is based on two Carleman-type inequalities.”
An alternative approach to regularity for the Navier–Stokes equations in critical spaces (2009, methodology): “7, proved in [12, 13] (see also [14]), and 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.”
Global Solvability of the Cauchy Problem for the Landau-Lifshitz-Gilbert Equation in Higher Dimensions (2011, result): “In case of heat flows this is a recent result, see [36], and motivated by parallel results for the Navier-Stokes equation, see [10].”
On the result of He concerning the smoothness of solutions to the Navier-Stokes equations (2003, unknown): “(I) u 2 Lt(I;Ls), 2t + 3 s 1, 2 t , 3 s 1 1 (see [13], for the case s = 3 see [12], [ 3 ])”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, background): “This result was later interpreted (and extended in a significant way) in [53] as a backward unique continuation one, in the absence of boundary conditions in the complement of a bounded set.”
Rigidity of asymptotically conical shrinking gradient Ricci solitons (2013, methodology): “Thus, as in [28], we introduce additional positive time dependent functions σ = σ(τ) and θ = θ(τ), stipulating only for the time-being that σ be increasing.”
The Navier-Stokes Equations in the Critical Lebesgue Space (2009, background): “Thanks to the backward uniqueness theorem proved in [5] (see also [6]), we reach ω(z) = 0 on (−T1, 0] × (R d \BR+3).”
L3,∞-solutions of the Navier-Stokes equations and backward uniqueness (2003, methodology): “Carleman-type inequalities The first Carleman-type inequality is essentially the same as that used in [5] and [6] (see also [3], [8], and [46]).”
On smoothness of L3,∞-solutions to the Navier–Stokes equations up to boundary (2005, background): “The main idea how to treat boundary regularity of L3,∞-solutions is similar to the case of interior regularity: reduction to a backward uniqueness problem for the heat operator, see [15], [ 2 ], and [4].”
Backwards uniqueness of the Ricci flow (2009, background): “zohata [M], Yamabe [Y], Lees-Protter [LP], Agmon-Nirenberg[AN], and Landis-Oleinik [LO], and extending through the work of Saut-Scheurer [SS], Lin [L], Sogge [So], Poon [Po], EscauriazaSverak-Veregin [ESV], and Escauriaza-Kenig-Ponce-Vega [EKPV] over the past two decades. Whereas modern eﬀorts have ”
Observability Inequalities and Measurable Sets (2012, background): “We begin with the following Carleman inequality (see [9] and [11]).”
Quantitative bounds for critically bounded solutions to the Navier-Stokes equations (2019, methodology): “However, in contrast to the more quantitative arguments of Leray, Prodi, Serrin and Ladyshenskaya, the proofs in the above references all rely at some point on a compactness argument to extract a limiting profile solution to which qualitative results such as unique continuation and backwards uniquen”
Uniqueness of Self-similar Shrinkers with Asymptotically Conical Ends (2011, methodology): “We basically follow the arguments in [15].”