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December  2015, 35(12): 5827-5867. doi: 10.3934/dcds.2015.35.5827

Unique continuation properties for relativistic Schrödinger operators with a singular potential

1. 

African Institute for Mathematical Sciences (A.I.M.S.) of Senegal, KM 2, Route de Joal, B.P. 1418, Mbour, Senegal

2. 

Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 55, 20125 Milano, Italy

Received  December 2013 Published  May 2015

Asymptotics of solutions to relativistic fractional elliptic equations with Hardy type potentials is established in this paper. As a consequence, unique continuation properties are obtained.
Citation: Mouhamed Moustapha Fall, Veronica Felli. Unique continuation properties for relativistic Schrödinger operators with a singular potential. Discrete & Continuous Dynamical Systems, 2015, 35 (12) : 5827-5867. doi: 10.3934/dcds.2015.35.5827
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Adv. Diff. Eq., 1 (1996), 241-264.  Google Scholar

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show all references

References:
[1]

Bull. Amer. Math. Soc., 8 (1983), 327-328. doi: 10.1090/S0273-0979-1983-15106-6.  Google Scholar

[2]

Probab. Math. Statist., 26 (2006), 155-173.  Google Scholar

[3]

Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 23-53. doi: 10.1016/j.anihpc.2013.02.001.  Google Scholar

[4]

Comm. Partial Differential Equations, 32 (2007), 1245-1260. doi: 10.1080/03605300600987306.  Google Scholar

[5]

Adv. Math., 226 (2011), 1410-1432. doi: 10.1016/j.aim.2010.07.016.  Google Scholar

[6]

Stochastic Process. Appl., 121 (2011), 1148-1172. doi: 10.1016/j.spa.2011.01.004.  Google Scholar

[7]

Bull. Sci. Math., 136 (2012), 521-573. doi: 10.1016/j.bulsci.2011.12.004.  Google Scholar

[8]

Vol. II, McGraw-Hill, New York, 1953.  Google Scholar

[9]

Comm. Partial Differential Equations, 39 (2014), 354-397. doi: 10.1080/03605302.2013.825918.  Google Scholar

[10]

Journal of the European Mathematical Society, 13 (2011), 119-174. doi: 10.4171/JEMS/246.  Google Scholar

[11]

Discrete Contin. Dynam. Systems, 32 (2012), 3895-3956. doi: 10.3934/dcds.2012.32.3895.  Google Scholar

[12]

Milan J. Math., 80 (2012), 203-226. doi: 10.1007/s00032-012-0174-y.  Google Scholar

[13]

Math. Methods Appl. Sci., published online, (2015). doi: 10.1002/mma.3438.  Google Scholar

[14]

Comm. Pure Appl. Math., 60 (2007), 1691-1705. doi: 10.1002/cpa.20186.  Google Scholar

[15]

Comm. Math. Phys., 274 (2007), 1-30. doi: 10.1007/s00220-007-0272-9.  Google Scholar

[16]

Indiana Univ. Math. J., 35 (1986), 245-268. doi: 10.1512/iumj.1986.35.35015.  Google Scholar

[17]

2nd edition, Grundlehren, 224, Springer, Berlin-Heidelberg-New York-Tokyo, 1983. doi: 10.1007/978-3-642-61798-0.  Google Scholar

[18]

Comm. Math. Phys., 53 (1977), 285-294.  Google Scholar

[19]

Ann. of Math. (2), 121 (1985), 463-494. doi: 10.2307/1971205.  Google Scholar

[20]

J. Eur. Math. Soc. (JEMS), 16 (2014), 1111-1171. doi: 10.4171/JEMS/456.  Google Scholar

[21]

Bull. Amer. Math. Soc. (N.S.), 22 (1990), 1-49. doi: 10.1090/S0273-0979-1990-15831-8.  Google Scholar

[22]

2nd edition, Graduate Studies in Mathematics, 14, American Mathematical Society, Providence, RI, 2001. doi: 10.1090/gsm/014.  Google Scholar

[23]

Pitman Research Notes in Math., Vol. 219, Longman 1990.  Google Scholar

[24]

Comm. Partial Differential Equations, 40 (2015), 77-114. doi: 10.1080/03605302.2014.905594.  Google Scholar

[25]

Proc. Amer. Math. Soc., 143 (2015), 1661-1664. doi: 10.1090/S0002-9939-2014-12594-9.  Google Scholar

[26]

Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J. 1970.  Google Scholar

[27]

Comm. Partial Differential Equations, 35 (2010), 2092-2122. doi: 10.1080/03605301003735680.  Google Scholar

[28]

Discrete Contin. Dyn. Syst., 31 (2011), 975-983. doi: 10.3934/dcds.2011.31.975.  Google Scholar

[29]

Adv. Diff. Eq., 1 (1996), 241-264.  Google Scholar

[30]

Geom. Funct. Anal., 2 (1992), 225-284. doi: 10.1007/BF01896975.  Google Scholar

[31]

J. Funct. Anal., 168 (1999), 121-144. doi: 10.1006/jfan.1999.3462.  Google Scholar

[32]

R. Yang, On higher order extensions for the fractional Laplacian, preprint,, , ().   Google Scholar

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