# Null-control and measurable sets

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 1, page 239-254
- ISSN: 1292-8119

## Access Full Article

top## Abstract

top## How to cite

topApraiz, Jone, and Escauriaza, Luis. "Null-control and measurable sets." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 239-254. <http://eudml.org/doc/272947>.

@article{Apraiz2013,

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

author = {Apraiz, Jone, Escauriaza, Luis},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {null-controllability; interior and boundary null-controllability},

language = {eng},

number = {1},

pages = {239-254},

publisher = {EDP-Sciences},

title = {Null-control and measurable sets},

url = {http://eudml.org/doc/272947},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Apraiz, Jone

AU - Escauriaza, Luis

TI - Null-control and measurable sets

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 1

SP - 239

EP - 254

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

LA - eng

KW - null-controllability; interior and boundary null-controllability

UR - http://eudml.org/doc/272947

ER -

## References

top- [1] L. Ahlfors and L. Bers, Riemann’s mapping theorem for variable metrics. Ann. Math.72 (1960) 265–296. Zbl0104.29902MR115006
- [2] G. Alessandrini and L. Escauriaza, Null-controllability of one-dimensional parabolic equations. ESAIM : COCV 14 (2008) 284–293. Zbl1145.35337MR2394511
- [3] K. Astala, Area distortion under quasiconformal mappings. Acta Math.173 (1994) 37–60. Zbl0815.30015MR1294669
- [4] A. Benabdallah and M.G. Naso, Null controllability of a thermoelastic plate. Abstr. Appl. Anal.7 (2002) 585–599. Zbl1013.35008MR1945447
- [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. Zbl1115.35055MR2310670
- [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. Zbl0067.32503MR76981
- [7] L. Bers, F. John and M. Schechter, Partial Differential Equations. Interscience. New York (1964). Zbl0126.00207MR163043
- [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. Zbl1242.35067MR2886465
- [9] L.C. Evans, Partial differential equations. American Mathematical Society, Providence, RI (1998). Zbl1194.35001MR1625845
- [10] A. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations. Seoul National University, Korea. Lect. Notes Ser. 34 (1996). Zbl0862.49004MR1406566
- [11] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Princeton University Press (1983). Zbl0516.49003MR717034
- [12] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition. Springer-Verlag (1983). Zbl0361.35003MR737190
- [13] F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations. Interscience Publishers, Inc., New York (1955). Zbl0464.35001MR75429
- [14] F. John, Partial Differential Equations. Springer-Verlag, New York (1982). Zbl0472.35001MR514404
- [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. Zbl1185.35153MR2593342
- [16] G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur. Commun. Partial Differ. Equ.20 (1995) 335–356. Zbl0819.35071MR1312710
- [17] G. Lebeau and E. Zuazua, Null controllability of a system of linear thermoelasticity. Arch. Rational Mech. Anal.141 (1998) 297–329. Zbl1064.93501MR1620510
- [18] E. Malinnikova, Propagation of smallness for solutions of generalized Cauchy-Riemann systems. Proc. Edinb. Math. Soc.47 (2004) 191–204. Zbl1061.31007MR2064745
- [19] A.I. Markushevich, Theory of Functions of a Complex Variable. Prentice Hall, Englewood Cliffs, NJ (1965). Zbl0135.12002
- [20] L. Miller, On the controllability of anomalous diffusions generated by the fractional laplacian. Math. Control Signals Syst.3 (2006) 260–271. Zbl1105.93015MR2272076
- [21] C.B. Morrey, Multiple Integrals in the Calculus of Variations. Springer (1966). Zbl1213.49002
- [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. Zbl0082.09402MR89334
- [23] N.S. Nadirashvili, A generalization of Hadamard’s three circles theorem. Mosc. Univ. Math. Bull.31 (1976) 30–32. Zbl0352.31002
- [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. Zbl0433.35006MR531646
- [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. Zbl1262.35206
- [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. Zbl1218.35054MR2772083
- [27] D.L. Russel, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Stud. Appl. Math.52 (1973) 189–221. Zbl0274.35041MR341256
- [28] S. Vessella, A continuous dependence result in the analytic continuation problem. Forum Math.11 (1999) 695–703. Zbl0933.35192MR1724631
- [29] H.F. Weinberger, A first course in partial differential equations with complex variables and transform methods. Dover Publications, New York (1995). Zbl0127.04805MR1351498

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.