Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems

By Oleg Yu. Imanuvilov, Jean-Pierre Puel. 2002

85 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e8c77c239363642fc3c36904abc25427f512868

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In Computational Theory and Mathematics

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Citations in the corpus

Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, methodology): “The following Carleman estimate was proved in [98] (see also [96], [97] for an extension to non-homogeneous boundary conditions).”
Carleman estimates for parabolic equations with nonhomogeneous boundary conditions (2009, methodology): “Applying the Carleman estimate for elliptic equations obtained in [12] and using (4.”
Observation and Control for Operator Semigroups (2009, background): “More sophisticated versions of Carleman estimates are currently applied to quite general linear partial differential operators (see, for instance, Hörmander [103], Fursikov and Imanuvilov [69], Tataru [214], [216], Imanuvilov and Puel [106] and Lebeau and Robbiano [151], [152]).”
Carleman estimates for one-dimensional degenerate heat equations (2006, background): “Controllability properties of nondegenerate parabolic equations have been widely studied in recent years; concerning the heat equation, see in particular [2, 5, 10, 13, 14, 15, 16, 17, 19, 24, 25, 27, 28, 29, 32, 33]; concerning the Stokes and Navier-Stokes equations, see in particular [3, 18, 19, 2”
Global Carleman estimate for stochastic parabolic equations, and its application (2014, background): “In order to obtain some estimate on the pressure in linearized Navier−Stokes equations in the context of controllability problems, a global Carleman estimate for elliptic operators with nonhomogeneous Dirichlet boundary conditions was established in [8].”