Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients

By Herbert Koch, D. Tataru. 2007

80 citations recorded by the source corpus.

In this work we obtain strong unique continuation results for variable coefficient second order parabolic equations. The coefficients in the principal part are assumed to satisfy a Lipschitz condition in x and a Hölder condition in time. The coefficients in the lower order terms, i.e., the potential and the gradient potential, are allowed to be unbounded and required only to satisfy mixed norm bounds in scale invariant spaces.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8d9afeda4d3a1b6813ef3cef530a0f8d5d219edf

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In Applied Mathematics

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

In Mathematical Physics

1. Jone Apraiz
2. C. Zhang
3. G. Wang
4. Luis Escauriaza
5. G A Seregin
6. Vladimír Sverák
7. F. J. Fernández
8. Lu Wang

Citations in the corpus

• 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, 40].”