@article{ASNSP_1994_4_21_4_595_0,
author = {Vel\'azquez, J. J. L.},
title = {Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {595--628},
year = {1994},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 21},
number = {4},
mrnumber = {1318773},
zbl = {0926.35023},
language = {en},
url = {https://www.numdam.org/item/ASNSP_1994_4_21_4_595_0/}
}
TY - JOUR AU - Velázquez, J. J. L. TI - Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1994 SP - 595 EP - 628 VL - 21 IS - 4 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1994_4_21_4_595_0/ LA - en ID - ASNSP_1994_4_21_4_595_0 ER -
%0 Journal Article %A Velázquez, J. J. L. %T Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1994 %P 595-628 %V 21 %N 4 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1994_4_21_4_595_0/ %G en %F ASNSP_1994_4_21_4_595_0
Velázquez, J. J. L. Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 21 (1994) no. 4, pp. 595-628. https://www.numdam.org/item/ASNSP_1994_4_21_4_595_0/
[AlAG] - - , Motion by Mean Curvature through singularities for surfaces of rotation. Preprint (1991).
[AG] - , Shortening space curves and flow through singularities. IMA Preprint 823 (1991). | MR
[A1] , Parabolic equations for curves on surfaces. Part. I, Ann. Math. 132 (1990), 451-483. | Zbl | MR
[A2] , Parabolic equations for curves on surfaces. Part. II, Ann. Math. 133 (1991), 171-215. | Zbl | MR
[A3] , On the formation of singularities in the curve shortening flow. J. Differential Geom. 33 (1991), 601-633. | Zbl | MR
[A4] , Some recent results on Mean Curvature Flow. In: Recent Advances in PDE's. M.A. Herrero - E. Zuazua eds., Research in Applied Math., Masson & J. Wiley, 1994, 1-18. | Zbl | MR
[AV1] - , Nonconvex collapse at rotationally symmetric hypersurfaces evolving by mean curvature flow. In preparation.
[AV2] - , Asymptotic shape of cusp singularities in curve shortening. Duke Math. J., in press. | Zbl | MR
[BDGG] - - , Minimal cones and the Bernstein problem. Inv. Math. 7 (1969), 243-268. | Zbl | MR
[B] , The motion of a surface by its mean curvature. Princeton University Press, Math. Notes, Princeton, New Jersey, 1978. | Zbl | MR
[B1] , On the asymptotic shape of blow-up. Indiana Univ. Math. J. 39 (1990), 947-960. | Zbl | MR
[B2] , Stable blow-up patterns. J. Differential Equations. 98 (1992), 57-75. | Zbl | MR
[BQ] - , The existence of bounded solutions of a semilinear heat equation. J. Differential Equations 82 (1989), 207-218. | Zbl | MR
[CGG] - - , Uniqueness and existence of viscosity solutions of generalized mean curvature flow. J. Differential Geom. 33 (1991), 749-786. | Zbl | MR
[DG] , Some conjectures on flow by mean curvature. Preprint.
[ESS] - - , Phase Transitions and generalized mean curvature flow equations. To appear in Comm. Pure Appl. Math. | MR
[ES] - , Motion of level sets by mean curvature I. J. Differential Geom. 33 (1991), 635-681. | Zbl | MR
[F] , Geometric measure theory. Springer Verlag, New York, 1969. | Zbl | MR
[FK] - , Refined asymptotics for the blow-up of u t-Δu=up. Comm. Pure Appl. Math. 45 (1992), 821-869. | Zbl
[FL] - , On the blow-up of a multidimensional semilinear heat equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 313-344. | Zbl | MR | Numdam
[GH] - , The heat equation shrinking plane convex curves. J. Differential Geom. 23 (1986), 69-96. | Zbl | MR
[GP] - , The equation ut=uxx +uB. Localization, asymptotic behaviour of unbounded solutions, Preprint N. 97, , Inst. Appl. Math. (1985), (in russian). | MR
[GaP] - , Quantum Mechanics. Vol. I (1990) and vol. II (1991), Springer Verlag. | Zbl
[G] , Minimal surfaces and functions of bounded variation. Birkhäuser, Boston, 1984. | Zbl | MR
[GK1] - , Asymptotically self-similar blow-up of semilinear heat equations. Comm. Pure Appl. Math. 38 (1985), 297-319. | Zbl | MR
[GK2] - , Characterizing blow-up using similarity variables. Indiana Univ. Math. J. 36 (1987), 1-40. | Zbl | MR
[GK3] - , Nondegeneracy of blow-up for semilinear heat equations. Comm. Pure Appl. Math. 42 (1987), 845-884. | Zbl | MR
[Gr] , The heat equation shrinks embedded plane curves to round points. J. Differential Geom. 26 (1987), 285-314. | Zbl | MR
[HV1] - , Blow-up behaviour of one-dimensional semilinear parabolic equations. Ann. Inst. Henri Poincaré 10 (1993), 131-189. | Zbl | MR | Numdam
[HV2] - , Flat blow-up in one-dimensional semilinear heat equations. Differential Integral Equations 5 (1992), 973-998. | Zbl | MR
[HV3] - , Blow-up profiles in one-dimensional semilinear parabolic problems. Comm. Partial Differential Equations 17 (1992), 205-219. | Zbl | MR
[HV4] - , Generic behaviour of one-dimensional blow-up patterns. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. 19 (1992), 381-450. | Zbl | MR | Numdam
[HV5] - , Generic behaviour near blow-up points for a N-dimensional semilinear heat equation. In preparation.
[HV6] - , A blow-up result for semilinear heat equations in the supercritical case. To appear.
[HV7] - , Explosion de solutions d'equations paraboliques semilinéaires supercritiques. C.R. Acad. Sci. Paris 319 (1994), 141-145. | Zbl | MR
[H] , Asymptotic behaviour for singularities of the mean curvature flow. J. Differential Geom. 31 (1991), 285-299. | Zbl | MR
[LSU] - - , Linear and quasilinear equations of parabolic type, Translations of Mathematical monographs, A.M.S. vol. 23, 1988. | Zbl
[L] , Countable spectrum at eigenfunctions of a nonlinear heat conduction equation with distributed parameters. Differentsial'nye Uravneiya 24, 7 (1988), 1226-1234. | Zbl | MR
[RS] - , Functional analysis, vol. II, Academic Press (1980). | MR
[S] , Minimal varieties in riemannian manifolds. Ann. of Math. 88 (1968), 62-106. | Zbl | MR
[So] , Motion of a set by the curvature of its boundary. J. Differential Equations 101 (1993), 313-372. | Zbl | MR
[T] , The existence of bounded solutions of a semilinear heat equation. SIAM J. Math. Anal. vol. 18, 2 (1987), 332-336. | Zbl | MR
[V1] , Classification of singularities for blowing up solutions in higher dimensions. Trans. Amer. Math. Soc. 338 (1993), 441-464. | Zbl | MR
[V2] , Higher dimensional blow-up for semilinear parabolic equations. Comm. Partial Differential Equations 17 (1992), 1567-1596. | Zbl | MR
[V3] , Estimates on the (N-1)-dimensional Hausdorff measure of the blow-up set for a semilinear heat equation. Indiana Univ. Math. J. 42 (1993), 446-476. | Zbl | MR
[V4] , Blow-up for semilinear parabolic equations. In Recent Advances in PDE's, M.A. Herrero - E. Zuazua eds., Research in Applied Math., Masson & J. Wiley, 1994, 131-145. | Zbl | MR





