[Amb] L. Ambrosio, Geometric evolution problems, distance function and viscosity solutions. Calculus of variations and partial differential equations (Pisa, 1996), 5–93,
Springer, Berlin, 2000.
[AM] L. Ambrosio and C. Mantegazza, Curvature and distance function from a manifold.
Dedicated to the memory of Fred Almgren. J. Geom. Anal. 8 (1998), no. 5, 723–
748.
[AS] L. Ambrosio and H. M. Soner, Level set approach to mean curvature flow in arbitrary codimension. J. Differential Geom. 43 (1996), no. 4, 693–737.
[An] S. B. Angenent, Shrinking doughnuts. In: Nonlinear diffusion equations and their
equilibrium states, eds., N. G. Lloyd, W. M. Ni, L. A. Peletier and J. Serrin 3,
Birkh¨
auser, Basel-Boston-Berlin, 1992. pp. 21–38.
[BG] G. Barles and C. Georgelin, A simple proof of convergence for an approximation
scheme for computing motions by mean curvature. SIAM J. Numer. Anal. 32
(1995), 484–500.
24
[CGG] Y.-G. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions
of generalized mean curvature flow equations. J. Differential Geom. 33 (1991), 749–
786.
[CIL] M. G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of
second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992),
1–67.
[ES] L. C. Evans and J. Spruck, Motion of level sets by mean curvature. I. J. Differential
Geom. 33 (1991), 635–681.
[Fo]
N. Forcadel, Dislocation dynamics with a mean curvature term: short time existence and uniqueness. Differential Integral Equations 21 (2008), 285–304.
[G]
Y. Giga, Surface Evolution Equations. A Level Set Approach. Monographs in
Mathematics, 99. Birkh¨
auser, Basel-Boston-Berlin, 2006. xii+264 pp.
[GG1] Y. Giga and S. Goto, Geometric evolution of phase-boundaries. On the evolution
of phase boundaries (Minneapolis, MN, 1990–91), 51–65, IMA Vol. Math. Appl.,
43, Springer, New York, 1992.
[GG] Y. Giga and S. Goto, Motion of hypersurfaces and geometric equations. J. Math.
Soc. Japan 44 (1992), 99–111.
[GGIS] Y. Giga and S. Goto, H. Ishii and M.-H. Sato, Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded
domains. Indiana Univ. Math. Journal 40 (1991), 443–470.
[GP] Y. Giga and N. Poˇz´
ar, Viscosity solutions for the crystalline mean curvature flow
with a nonuniform driving force term. SN Partial Differ. Equ. Appl. 1 (2020),
Article number: 39.
[GTZ] Y. Giga, H. V. Tran and L. Zhang, On obstacle problem for mean curvature flow
with driving force. Geom. Flows 4 (2019), 9–29.
[GT] D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order.
Reprint of the 1998 edition. Classics in Mathematics. Springer-Verlag, Berlin, 2001.
xiv+517 pp.
[GNO] S. Goto, M. Nakagawa and T. Ohtsuka, Uniqueness and existence of generalized
motion for spiral crystal growth. Indiana Univ. Math. J. 57 (2008), no. 5, 2571–
2599.
[Gr87] M. A. Grayson, The heat equation shrinks embedded plane curves to round points.
J. Differential Geom. 26 (1987), no. 2, 285–314.
[Gr89] M. A. Grayson, A short note on the evolution of a surface by its mean curvature.
Duke Math. J. 58 (1989), no. 3, 555–558.
[KP] S. G. Krantz and H. R. Parks, The implicit function theorem. History, theory, and applications. Reprint of the 2003 edition. Modern Birkh¨
auser Classics.
Birkh¨
auser/Springer, New York, 2013. xiv+163 pp.
[M]
G. Mercier, Mean curvature flow with obstacles: a viscosity approach. https:
//arxiv.org/abs/1409.7657
[OGT] T. Ohtsuka, Y.-H. R. Tsai and Y. Giga, A level set approach reflecting sheet
structure with single auxiliary function for evolving spirals on crystal surfaces. J.
Sci. Comput. 62 (2015), no. 3, 831–874.
25
[SZ]
P. Sternberg and W. P. Ziemer, Generalized motion by curvature with a Dirichlet
condition. J. Differential Equations 114 (1994), 580–600.
[Ya]
N. Yamada, Viscosity solutions for a system of elliptic inequalities with bilateral
obstacles. Funkcial. Ekvac. 30 (1987), 417–425.
26
...
論文の公開元へ
