Backward uniqueness for the heat operator in a half-space

St. Petersburg Mathematical Journal

Volumn 15, Issue 1, 2003, Pages 139-148

  Escauriaza, L ^a   Seregin, G ^b   Sverak V ^c  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Backward uniqueness; Heat operator

Indexed keywords

EID: 85009784256     PISSN: 10610022     EISSN: 15477371     Source Type: Journal    
DOI: 10.1090/S1061-0022-03-00806-9     Document Type: Article

References (12)

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. Šverák, On backward uniqueness for parabolic equations, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 288 (2002), 100–103.MR 2003i:35225
4. L. Escauriaza, G. Seregin, and V. Šverák, 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
8. English transl., Transl. Math. Monogr., vol. 23, Amer. Math. Soc., Providence, RI, 1968.MR 39:3159a
9. 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
10. 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
11. G. Seregin and V. Šverák, 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.
12. D. Tataru, Carleman estimates, unique continuation, and applications, Notes downloadable from http://math.berkeley.edu/tataru/ucp.html.