Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
Jérôme Le Rousseau[1]; Nicolas Lerner[2]
- [1] MAPMO, UMR CNRS 6628, Route de Chartres, Université d’Orléans B.P. 6759 – 45067 Orléans cedex 2 France
- [2] Projet analyse fonctionnelle, Institut de Mathématiques de Jussieu, UMR CNRS 7586, Université Pierre-et-Marie-Curie (Paris 6), Boîte 186 - 4, Place Jussieu - 75252 Paris cedex 05, France
Journées Équations aux dérivées partielles (2010)
- page 1-23
- ISSN: 0752-0360
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top- S. Alinhac, Non-unicité pour des opérateurs différentiels à caractéristiques complexes simples, Ann. Sci. École Norm. Sup. (4) 13 (1980), 385-393 Zbl0456.35002MR597745
- A. Benabdallah, Y. Dermenjian, J. Le Rousseau, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem, J. Math. Anal. Appl. 336 (2007), 865-887 Zbl1189.35349MR2352986
- P. Buonocore, P. Manselli, Nonunique continuation for plane uniformly elliptic equations in Sobolev spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 29 (2000), 731-754 Zbl1072.35049MR1822406
- A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations., Amer. J. Math. 80 (1958), 16-36 Zbl0080.30302MR104925
- T. Carleman, Sur un problème d’unicité pur les systèmes d’équations aux dérivées partielles à deux variables indépendantes, Ark. Mat., Astr. Fys. 26 (1939) Zbl0022.34201
- A. Doubova, A. Osses, J.-P. Puel, Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients, ESAIM Control Optim. Calc. Var. 8 (2002), 621-661 Zbl1092.93006MR1932966
- L. Hörmander, On the uniqueness of the Cauchy problem, Math. Scand. 6 (1958), 213-225 Zbl0088.30201MR104924
- L. Hörmander, Linear partial differential operators, (1963), Academic Press Inc., Publishers, New York Zbl0108.09301MR161012
- L. Hörmander, The analysis of linear partial differential operators. IV, 275 (1994), Springer-Verlag, Berlin Zbl0612.35001MR1481433
- O. Yu. Imanuvilov, J.-P. Puel, Global Carleman estimates for weak solutions of Elliptic nonhomogeneous Dirichlet problems, Int. Math. Res. Not. 16 (2003), 883-913 Zbl1146.35340MR1959940
- J. Le Rousseau, Carleman estimates and controllability results for the one-dimensional heat equation with coefficients, J. Differential Equations 233 (2007), 417-447 Zbl1128.35020MR2292514
- J. Le Rousseau, G. Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations, Preprint (2009) Zbl1262.35206
- J. Le Rousseau, N. Lerner, Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions, in prep. (2010)
- J. Le Rousseau, L. Robbiano, Carleman estimate for elliptic operators with coefficents with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations, Arch. Rational Mech. Anal. 195 (2010), 953-990 Zbl1202.35336MR2591978
- J. Le Rousseau, L. Robbiano, Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces, Invent. Math, to appear (2010) Zbl1218.35054
- N. Lerner, Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators, (2010), Birkhäuser, Basel Zbl1186.47001MR2599384
- K. Miller, Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Hölder continuous coefficients, Arch. Rational Mech. Anal. 54 (1974), 105-117 Zbl0289.35046MR342822
- A. Pliś, On non-uniqueness in Cauchy problem for an elliptic second order differential equation, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 11 (1963), 95-100 Zbl0107.07901MR153959
- F. Schulz, On the unique continuation property of elliptic divergence form equations in the plane, Math. Z. 228 (1998), 201-206 Zbl0905.35020MR1630571