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

@article{COCV_2013__19_1_239_0, author = {Apraiz, Jone and Escauriaza, Luis}, title = {Null-control and measurable sets}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {239--254}, publisher = {EDP-Sciences}, volume = {19}, number = {1}, year = {2013}, doi = {10.1051/cocv/2012005}, mrnumber = {3023068}, zbl = {1262.35118}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2012005/} }

TY - JOUR AU - Apraiz, Jone AU - Escauriaza, Luis TI - Null-control and measurable sets JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 239 EP - 254 VL - 19 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012005/ DO - 10.1051/cocv/2012005 LA - en ID - COCV_2013__19_1_239_0 ER -

%0 Journal Article %A Apraiz, Jone %A Escauriaza, Luis %T Null-control and measurable sets %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 239-254 %V 19 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012005/ %R 10.1051/cocv/2012005 %G en %F COCV_2013__19_1_239_0

Apraiz, Jone; Escauriaza, Luis. Null-control and measurable sets. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 1, pp. 239-254. doi : 10.1051/cocv/2012005. http://www.numdam.org/articles/10.1051/cocv/2012005/

[1] Riemann's mapping theorem for variable metrics. Ann. Math. 72 (1960) 265-296. | MR | Zbl

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

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

,[4] Null controllability of a thermoelastic plate. Abstr. Appl. Anal. 7 (2002) 585-599. | MR | Zbl

and ,[5] 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 | Zbl

, and ,[6] 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 | Zbl

and ,[7] Partial Differential Equations. Interscience. New York (1964). | MR | Zbl

, and ,[8] 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 | Zbl

, and ,[9] Partial differential equations. American Mathematical Society, Providence, RI (1998). | MR | Zbl

,[10] Controllability of Evolution Equations. Seoul National University, Korea. Lect. Notes Ser. 34 (1996). | MR | Zbl

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

,[12] Elliptic Partial Differential Equations of Second Order, 2nd edition. Springer-Verlag (1983). | MR | Zbl

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

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

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

,[16] Contrôle exact de l'équation de la chaleur. Commun. Partial Differ. Equ. 20 (1995) 335-356. | MR | Zbl

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

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

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

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

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

,[22] On the analyticity of the solutions of linear elliptic systems of partial differential equations. Commun. Pure Appl. Math. X (1957) 271-290. | MR | Zbl

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

,[24] 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 | Zbl

,[25] 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

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

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

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

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

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