Nonlinear diffusion with a bounded stationary level surface

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 27, Issue 3, 2010, Pages 937-952

  Magnanini, Rolando ^a   Sakaguchi, Shigeru ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Nonlinear diffusion equation; Overdetermined problems; Stationary level surfaces

Indexed keywords

CONTAINERS; DIFFUSION; PARTIAL DIFFERENTIAL EQUATIONS;

CHARACTERISTIC FUNCTIONS; CONSTANT DENSITY; HEAT FLOWS; HYPERBOLIC SPACES; NONLINEAR DIFFUSION; NONLINEAR DIFFUSION EQUATION; NONLINEAR DIFFUSION EQUATIONS; SUBDOMAIN;

NONLINEAR EQUATIONS;

EID: 77951258998     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2009.12.001     Document Type: Article

References (23)

1. Aleksandrov A.D. Uniqueness theorems for surfaces in the large V. Vestnik Leningrad Univ. 13 19 (1958) 5-8 English translation:
2. Aleksandrov A.D. Uniqueness theorems for surfaces in the large V. Amer. Math. Soc. Transl. Ser. 2 21 (1962) 412-415
3. Crandall M.G., Ishii H., and Lions P.-L. User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1-67
4. Evans L.C., and Ishii H. A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities. Ann. Inst. H. Poincaré 2 (1985) 1-20
5. Evans L.C., and Souganidis P.E. A PDE approach to certain large deviation problems for systems of parabolic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire S6 (1989) 229-258
6. Freidlin M.I., and Wentzell A.D. Random Perturbations of Dynamical Systems (1984), Springer-Verlag, New York
7. Gilding B.H. Hölder continuity of solutions of parabolic equations. J. London Math. Soc. 13 (1976) 103-106
8. Koike S. An asymptotic formula for solutions of Hamilton-Jacobi-Bellman equations. Nonlinear Anal. 11 (1987) 429-436
9. Kumaresan S., and Prajapat J. Serrin's result for hyperbolic space and sphere. Duke Math. J. 91 (1998) 17-28
10. Lions P.L., Souganidis P.E., and Vázquez J.L. The relation between the porous medium and the eikonal equations in several space dimensions. Rev. Mat. Iberoamericana 3 (1987) 275-310
11. Magnanini R., and Sakaguchi S. The spatial critical points not moving along the heat flow. J. Anal. Math. 71 (1997) 237-261
12. Magnanini R., and Sakaguchi S. The spatial critical points not moving along the heat flow II: The centrosymmetric case. Math. Z. 230 (1999) 695-712 Corrigendum:
13. Magnanini R., and Sakaguchi S. The spatial critical points not moving along the heat flow II: The centrosymmetric case. Math. Z. 232 (1999) 389
14. Magnanini R., and Sakaguchi S. Matzoh ball soup: Heat conductors with a stationary isothermic surface. Ann. of Math. 156 (2002) 931-946
15. Magnanini R., and Sakaguchi S. Interaction between degenerate diffusion and shape of domain. Proc. Royal Soc. Edinburgh Sect. A 137 (2007) 373-388
16. Magnanini R., and Sakaguchi S. Stationary isothermic surfaces for unbounded domains. Indiana Univ. Math. J. 56 (2007) 2723-2738
17. Norris J.R. Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds. Acta Math. 179 (1997) 79-103
18. Reichel W. Radial symmetry for elliptic boundary-value problems on exterior domains. Arch. Rational Mech. Anal. 137 (1997) 381-394
19. Reilly R.C. Mean curvature, the Laplacian, and soap bubbles. Amer. Math. Monthly 89 (1982) 180-188 197-198
20. Serrin J. A symmetry problem in potential theory. Arch. Rational Mech. Anal. 43 (1971) 304-318
21. Sirakov B. Symmetry for exterior elliptic problems and two conjectures in potential theory. Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001) 135-156
22. Strömberg T. The Hopf-Lax formula gives the unique viscosity solution. Differential Integral Equations 15 (2002) 47-52
23. Varadhan S.R.S. On the behavior of the fundamental solution of the heat equation with variable coefficients. Comm. Pure Appl. Math. 20 (1967) 431-455