Singular degenerate parabolic equations with applications to the p-Laplace diffusion equation

Communications in Partial Differential Equations

Volumn 22, Issue 3-4, 1997, Pages 381-441

  Ohnuma, Masaki ^a   Sato, Koh ^b  

^a HOKKAIDO UNIVERSITY   (Japan)

^b OTARU UNIVERSITY OF COMMERCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000130437     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309708821268     Document Type: Article

References (15)

1. G. Barles and B. Perthame. Discontinuous solutions of deterministic optimal stoppiny-time problems. Modèl. Math. Anal. Num., 21 (1987), 557-570.
2. Y.-G. Chen, Y. Giga, and S. Goto. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Diff. Geometry, 33 (1991), 749-786.
3. M. G. Crandall and H. Ishii. The maximum principle for semicontinuons functions. Diff. Int. Equations, 3 (1990), 1001-1014.
4. M. G. Crandall, H. Isliii, and P.-L. Lions. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc., 27 (1992), 1-67.
5. E. DiBenedetto. Degenerate parabolic equations. Springer-Verlag, New York, 1993.
6. L. C. Evans and J. Spruck. Motion of level sets by mean curvature I. J. Diff. Geometry, 33 (1991), 635-681.
7. Y. Giga. Motion of a graph by converified energy. Hokkaido Math. J., 23 (1994),185-212.
8. S. Goto. Generalized motion of hypersurfaces whose growth, speed depends superlinearly on the curvature tensor. Diff. Int. Equations. 7 (1994), 323-343.
9. M. E. Gurtin, H. M. Soner, and P. E. Souganidis. Anisotropic, motion of an interface relaxed by formation of infinitesimal wrinkles. J. Diff. Equations, 119 (1995), 54-108.
10. M. Ôtani. A Remark on Nonlinear Elliptic Equations . Proc. Fac. Sci. Tokai Univ., 19 (1984), 23-28.
11. M. Ôtani. On Certain Second Order Ordinary Differential Equations Associated with Sobolev-Poicaré-type Inequalitics . Nonlinear Anal. T.M.A, 8 (1984),1255-1270.
12. H. Ishii. Degenerate parabolic PDEs with, discontinuities and generalized evolution of surfaces. Advances in Differential Equations., 1 (1996),51-72.
13. H. Ishii and P. E. Souganidis. Generalized motion of noncompact hypersurfaces with, velocity having arbitrary growth, on the curvature tensor. Tôhoku Math. J., 47 (1995), 227-250.
14. J.-L. Lions. Quelques méthodes de resolution des problèms aux limites non linéaires. Dunod, Paris, 1969.
15. M. Ohnuma and M.-H. Sato. Singular degenerate, parabolic equations with, applications to geometric evolution equations. Diff. Int. Equations, 6 (1993),1265-1280.