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St. Petersburg Mathematical Journal

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Backward uniqueness for the heat operator in a half-space

Authors: L. Escauriaza, G. Seregin and V. Sverák
Translated by:
Original publication: Algebra i Analiz, tom 15 (2003), nomer 1.
Journal: St. Petersburg Math. J. 15 (2004), 139-148
MSC (2000): Primary 35K10
Published electronically: December 31, 2003
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Abstract: A backward uniqueness result is proved for the heat operator with variable lower order terms in a half-space. The main point of the result is that the boundary conditions are not controlled by the assumptions.

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  • [1] L. Escauriaza, Carleman inequalities and the heat operator, Duke Math. J. 104 (2000), no. 1, 113-127. MR 2001m:35135
  • [2] L. Escauriaza and F. J. Fernández, Unique continuation for parabolic operators (to appear).
  • [3] L. Escauriaza, G. Seregin, and V. Sverák, On backward uniqueness for parabolic equations, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 288 (2002), 100-103. MR 2003i:35225
  • [4] -, On backward uniqueness for parabolic equations, Arch. Rational Mech. Anal. (to appear).
  • [5] L. Escauriaza and L. Vega, Carleman inequalities and the heat operator. II, Indiana Univ. Math. J. 50 (2001), 1149-1169. MR 2003b:35088
  • [6] L. Hörmander, Linear partial differential operators, Grundlehren Math. Wiss., vol. 116, Springer-Verlag, Berlin, etc., 1963. MR 28:4221
  • [7] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and quasilinear equations of parabolic type, ``Nauka'', Moscow, 1967; English transl., Transl. Math. Monogr., vol. 23, Amer. Math. Soc., Providence, RI, 1968. MR 39:3159a
  • [8] S. Micu and E. Zuazua, On the lack of null-controllability of the heat equation on the half-space, Port. Math. (N.S.) 58 (2001), no. 1, 1-24. MR 2002a:93011
  • [9] G. Seregin, Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary, J. Math. Fluid Mech. 4 (2002), no. 1, 1-29. MR 2003a:35152
  • [10] G. Seregin and V. Sverák, The Navier-Stokes equations and backward uniqueness, Nonlinear Problems of Mathematical Physics and Related Topics. Vol. 2 (in Honor of Prof. O. A. Ladyzhenskaya), Kluwer Acad./Plenum Publ., 2002, pp. 359-370.
  • [11] D. Tataru, Carleman estimates, unique continuation, and applications, Notes downloadable from

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Additional Information

L. Escauriaza
Affiliation: Dipartimento di Matemáticas, UPV/EHU, Bilbao, Spain

G. Seregin
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191011, Russia

V. Sverák
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, MN

Keywords: Backward uniqueness, heat operator
Received by editor(s): September 2, 2002
Published electronically: December 31, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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