Null-control and measurable sets
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 239-254.

We prove the interior and boundary null-controllability of some parabolic evolutions with controls acting over measurable sets.

DOI : https://doi.org/10.1051/cocv/2012005
Classification : 35B37
Mots clés : null-controllability
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     title = {Null-control and measurable sets},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {239--254},
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     url = {http://www.numdam.org/articles/10.1051/cocv/2012005/}
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Apraiz, Jone; Escauriaza, Luis. Null-control and measurable sets. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 239-254. doi : 10.1051/cocv/2012005. http://www.numdam.org/articles/10.1051/cocv/2012005/

[1] L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics. Ann. Math. 72 (1960) 265-296. | MR 115006 | Zbl 0104.29902

[2] G. Alessandrini and L. Escauriaza, Null-controllability of one-dimensional parabolic equations. ESAIM : COCV 14 (2008) 284-293. | Numdam | MR 2394511 | Zbl 1145.35337

[3] K. Astala, Area distortion under quasiconformal mappings. Acta Math. 173 (1994) 37-60. | MR 1294669 | Zbl 0815.30015

[4] A. Benabdallah and M.G. Naso, Null controllability of a thermoelastic plate. Abstr. Appl. Anal. 7 (2002) 585-599. | MR 1945447 | Zbl 1013.35008

[5] A. Benabdallah, Y. Dermenjian and J. Le Rousseau, On the controllability of linear parabolic equations with an arbitrary control location for stratified media. C. R. Acad. Sci. Paris, Sér. 1 344 (2007) 357-362. | MR 2310670 | Zbl 1115.35055

[6] L. Bers and L. Nirenberg, On a representation theorem for linear elliptic systems with discontinuous coefficients and applications, in Convegno Internazionale sulle Equazioni alle Derivate Parziali. Cremonese, Roma (1955) 111-138. | MR 76981 | Zbl 0067.32503

[7] L. Bers, F. John and M. Schechter, Partial Differential Equations. Interscience. New York (1964). | MR 163043 | Zbl 0126.00207

[8] S. Cho, H. Dong and S. Kim, Global estimates for Green's matrix of second order parabolic systems with application to elliptic systems in two dimensional domains. Potential Anal. 36 (2012) 339-372. | MR 2886465 | Zbl 1242.35067

[9] L.C. Evans, Partial differential equations. American Mathematical Society, Providence, RI (1998). | MR 1625845 | Zbl 1194.35001

[10] A. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations. Seoul National University, Korea. Lect. Notes Ser. 34 (1996). | MR 1406566 | Zbl 0862.49004

[11] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Princeton University Press (1983). | MR 717034 | Zbl 0516.49003

[12] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition. Springer-Verlag (1983). | MR 737190 | Zbl 0361.35003

[13] F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations. Interscience Publishers, Inc., New York (1955). | MR 75429 | Zbl 0464.35001

[14] F. John, Partial Differential Equations. Springer-Verlag, New York (1982). | MR 514404 | Zbl 0472.35001

[15] M. Léautaud, Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems. J. Funct. Anal. 258 (2010) 2739-2778. | MR 2593342 | Zbl 1185.35153

[16] G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur. Commun. Partial Differ. Equ. 20 (1995) 335-356. | MR 1312710 | Zbl 0819.35071

[17] G. Lebeau and E. Zuazua, Null controllability of a system of linear thermoelasticity. Arch. Rational Mech. Anal. 141 (1998) 297-329. | MR 1620510 | Zbl 1064.93501

[18] E. Malinnikova, Propagation of smallness for solutions of generalized Cauchy-Riemann systems. Proc. Edinb. Math. Soc. 47 (2004) 191-204. | MR 2064745 | Zbl 1061.31007

[19] A.I. Markushevich, Theory of Functions of a Complex Variable. Prentice Hall, Englewood Cliffs, NJ (1965). | Zbl 0135.12002

[20] L. Miller, On the controllability of anomalous diffusions generated by the fractional laplacian. Math. Control Signals Syst. 3 (2006) 260-271. | MR 2272076 | Zbl 1105.93015

[21] C.B. Morrey, Multiple Integrals in the Calculus of Variations. Springer (1966). | Zbl 1213.49002

[22] C.B. Morrey and L. Nirenberg, On the analyticity of the solutions of linear elliptic systems of partial differential equations. Commun. Pure Appl. Math. X (1957) 271-290. | MR 89334 | Zbl 0082.09402

[23] N.S. Nadirashvili, A generalization of Hadamard's three circles theorem. Mosc. Univ. Math. Bull. 31 (1976) 30-32. | Zbl 0352.31002

[24] N.S. Nadirashvili, Estimation of the solutions of elliptic equations with analytic coefficients which are bounded on some set. Mosc. Univ. Math. Bull. 34 (1979) 44-48. | MR 531646 | Zbl 0433.35006

[25] J. Le Rousseau and G. Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations. ESAIM : COCV, doi:10.1051/cocv/2011168. | Numdam | Zbl 1262.35206

[26] J. Le Rousseau and L. Robbiano, Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces. Invent. Math. 183 (2011) 245-336. | MR 2772083 | Zbl 1218.35054

[27] D.L. Russel, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Stud. Appl. Math. 52 (1973) 189-221. | MR 341256 | Zbl 0274.35041

[28] S. Vessella, A continuous dependence result in the analytic continuation problem. Forum Math. 11 (1999) 695-703. | MR 1724631 | Zbl 0933.35192

[29] H.F. Weinberger, A first course in partial differential equations with complex variables and transform methods. Dover Publications, New York (1995). | MR 1351498 | Zbl 0127.04805

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