Carleman inequalities and the heat operator II

By Luis Escauriaza, Luis Vega. 2001

66 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/e2f2a0351d08d500b3100ec3045e38581b070b97

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. 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 Computational Theory and Mathematics

1. G A Seregin
2. D. Tataru
3. Herbert Koch
4. Vladimír Sverák
5. Luis Escauriaza
6. F. J. Fernández
7. Jone Apraiz
8. C. Zhang

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): “In this context the work of Thangavelu and Karadzhov has already found applications in Escauriaza [2] and EscauriazaVega [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].”
• Unique Continuation for Parabolic Operators. II (2003, background): “Thus, the function on the left hand side has a zero of infinite order at a ¼ 0 when the same occurs with uðx; 0Þ at x ¼ 0, and the arguments in Escauriaza and Vega (2001) show that this suffices to derive that uðx; 0Þ 0 in B2.”
• 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].”
• 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 .”
• Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients (2007, methodology): “n with the mixed norm LpLq Carleman estimates in the simplest case, i.e. with constant coefficients and a polynomial weight. These were proved in [1] except for the endpoint which was obtained later in [3] . After a conformal change of coordinates and conjugation with respect to the exponential weight”