Long-time vanishing properties of solutions of some semilinear parabolic equations
Annales de l'I.H.P. Analyse non linéaire, Volume 18 (2001) no. 1, p. 43-68
@article{AIHPC_2001__18_1_43_0,
     author = {Belaud, Yves and Helffer, Bernard and V\'eron, Laurent},
     title = {Long-time vanishing properties of solutions of some semilinear parabolic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {18},
     number = {1},
     year = {2001},
     pages = {43-68},
     zbl = {0983.35066},
     mrnumber = {1810270},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2001__18_1_43_0}
}
Belaud, Yves; Helffer, Bernard; Véron, Laurent. Long-time vanishing properties of solutions of some semilinear parabolic equations. Annales de l'I.H.P. Analyse non linéaire, Volume 18 (2001) no. 1, pp. 43-68. http://www.numdam.org/item/AIHPC_2001__18_1_43_0/

1 Belaud Y., Ph.D. Thesis, Université François Rabelais-Tours (in preparation).

2 Cwikel M, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. Math. Vol. 106 (1977) 93-100. | MR 473576 | Zbl 0362.47006

3 Evans L.C, Differentiability of a nonlinear semigroup in L1, J. Math. Anal. Appl. Vol. 60 (1977) 703-715. | MR 454360 | Zbl 0363.47032

4 Evans L.C, Gariepy R.F, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, 1992. | MR 1158660 | Zbl 0804.28001

5 Friedman A, Phillips D, The free boundary of a semilinear elliptic equation, Trans. Amer. Math. Soc. Vol. 282 (1984) 153-182. | MR 728708 | Zbl 0552.35079

6 Gidas B, Ni W.M, Nirenberg L, Symmetry and related properties via the maximum principle, Comm. Math. Phys. Vol. 68 (1979) 209-243. | MR 544879 | Zbl 0425.35020

7 Gilbarg D, Trudinger N, Elliptic Partial Differential Equations of Second Order, Springer, 1977. | MR 473443 | Zbl 0361.35003

8 Helffer B, Semi-classical analysis for the Schrödinger operator and applications, Lecture Notes in Math., Vol. 1336, Springer, 1989. | MR 960278 | Zbl 0647.35002

9 Helffer B, Sjöstrand J, Multiple wells in the semi-classical limit I, Comm. in P.D.E. Vol. 9 (1984) 337-408. | MR 740094 | Zbl 0546.35053

10 Kondratiev V, Véron L, Asymptotic behavior of the solutions of some parabolic or elliptic equations, Asymptotic Analysis Vol. 14 (1997) 117-156. | MR 1451209 | Zbl 0897.35013

11 Laptev A, Netrusov Yu, On the negative eigenvalues of a class of Schrödinger operators, Preprint, KTH, Stockholm, 1998. | MR 1730512

12 Lieb E.H, Thirring W, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relations to Sobolev inequalities, in: Studies in Math. Phys., Essays in Honour of V. Bargmann, Princeton Univ. Press, 1976. | Zbl 0342.35044

13 Lojaciewicz S, Ensembles Semi-Analytiques, Institut des Hautes Etudes Sci. Bures-sur-Yvette, France, 1964.

14 Lojaciewicz S, Sur les ensembles semi-analytiques, in: Actes Congrès Intern. Math. 1970, Tome 2, 1971, pp. 237-241. | MR 425152 | Zbl 0241.32005

15 Mazya V.G, Sobolev Spaces, Springer, 1985. | MR 817985 | Zbl 0692.46023

16 Moser J, A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. Vol. 13 (1960) 457-468. | MR 170091 | Zbl 0111.09301

17 Nash J, Continuity of solutions of parabolic equations, Amer. J. Math. Vol. 80 (1958) 931-954. | MR 100158 | Zbl 0096.06902

18 Rozenblyum G.V, Distribution of the discrete spectrum of singular differential operators, Doklady Akad. Nauk USSR Vol. 202 (1972) 1012-1015. | MR 295148 | Zbl 0249.35069

19 Whitney H, Local properties of analytic varieties, in: Cairns S.S (Ed.), Differential and Combinatorial Topology, 1965, pp. 205-244. | MR 188486 | Zbl 0129.39402