Carleman inequalities and the heat operator

By Luis Escauriaza. 2000

79 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e11369ce073331fdc2dcd7f878387dbccfa1842c

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In Applied Mathematics

1. Vladimír Sverák
2. D. Tataru
3. Herbert Koch
4. G A Seregin
5. Luis Escauriaza
6. F. J. Fernández
7. Terence Tao
8. Carlos E. Kenig

In Mathematical Physics

1. Vladimír Sverák
2. G A Seregin
3. D. Tataru
4. Terence Tao
5. Herbert Koch
6. Carlos E. Kenig
7. Luis Escauriaza
8. F. J. Fernández

Citations in the corpus

• L^p eigenfunction bounds for the Hermite operator (2004, background): “[2] Luis Escauriaza.”
• Observability Inequalities and Measurable Sets (2012, background): “These can be derived in the more general setting from the Carleman inequalities in [8, 9, 12, 15, 25] or from local versions of frequency function arguments [10, 39].”
• Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients (2007, background): “These bounds were essential in the proof of Lp Carleman inequalities for the heat operator of Escauriaza [8] and Escauriaza and Vega [10] which yield SUCP(I) when g = In, W = 0 and V ∈ L1L∞ + L∞Ln/2.”
• Unique Continuation for Parabolic Operators. II (2003, background): “In Escauriaza (2000), Escauriaza and Vega (2001), and Escauriaza and Fernández (to appear), Escauriaza, Vega, and the author proved some Carleman inequalities implying unique continuation properties for solutions to parabolic equations.”
• 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]).”
• Dispersive estimates for principally normal pseudodifferential operators (2004, background): “The counterpart of the Jerison-Kenig estimates for second order constant coefficient parabolic operators is proved in Escauriaza [3].”
• Unique continuation for parabolic operators (2003, methodology): “The strong unique continuation property for parabolic equations with timedependent coefficients is treated by Poon in [16], Chen [4] and Escauriaza and Vega in [5] and [6].”
• Backward Uniqueness for Parabolic Equations (2003, methodology): “The first Carleman inequality, based on ideas developed in [3], [4], [5], and [6], is used to prove that under the assumptions of Theorem 1 one has |u(x, t)|+ |∇u(x, t)| ≤ Ne−|x| 2/(Nt) for some N > 0 in Q6R,T .”