On the pointwise jump condition at the free boundary in the 1-phase Stefan problem

Communications on Pure and Applied Analysis

Volumn 4, Issue 2, 2005, Pages 357-366

  Danielli, Donatella ^a   Korten, Marianne ^b  

^a PURDUE UNIVERSITY   (United States)

^b KANSAS STATE UNIVERSITY   (United States)

Author keywords

Discontinuous solutions; Finite perimeter; Free boundaries; Jump condition; Level sets; Mushy regions; Stefan problem

Indexed keywords

EID: 33746535473     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2005.4.357     Document Type: Article

References (18)

1. [AmFuP] L. Ambrosio, N. Fusco and D. Pallara, "Functions of Bounded Variation and Free Discontinuity Problems", Oxford University Press, New York, 2000.
2. [AnKo] D. Andreucci and M.K. Korten, Initial traces of solutions to a one-phase Stefan problem in an infinite strip, Rev. Mat. Iberoamericana, (2) 9 (1993), 315-332.
3. [CaV] L.A. Caffarelli and J.L. Vázquez, A free-boundary problem for the heat equation arising in flame propagation, Trans. Am. Math. Soc. 347, 2 (1995), 411-441.
4. [CaJKe] L.A. Caffarelli, D. Jerison, C.E. Kenig, Global energy minimizers for free boundary problems and full regularity in three dimensions, Contemp. Math., 350, Amer. Math. Soc., Providence, RI, 2004.
5. [CaLeWo] L.A. Caffarelli, C. Lederman and N. Wolanski, Pointwise and viscosity solutions for the limit of a two phase parabolic singular perturbation problem, Indiana Univ. Math. Jour., (3) 46 (1997), 719-740.
6. 1,α regularity of the free boundary for the N-dimensional porous media equation, Comm. Pure Appl. Math., (7) 43 (1990), 885-902.
7. [ChFr] G.Q. Chen, H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Rational. Mech. Anal., (2) 147 (1999), 89-118.
8. [ChFr2] G.Q. Chen, H. Frid, On the theory of divergence-measure fields and its applications, Bol. Soc. Brasil. Mat. (N. S.), (3) 32 (2001), 401-133.
9. [Da] D. Danielli, A singular perturbation approach to a two phase parabolic free boundary problem arising in combustion theory, Diff. Int. Eqns., to appear.
10. [DeOWe] C. De Lellis, F. Otto, M. Westdickenberg, Structure of entropy solutions for multidimensional scalar conservation laws, Arch. Ration. Mech. Anal., (2) 170 (2003), 137-184.
11. [DiB] E. DiBenedetto, Continuity of weak solutions to certain singular parabolic equations, Ann. Mat. Pura Appl., (4) 130 (1982), 131-176.
12. +: Regularity and uniqueness for the Cauchy problem, Nonl. Anal., Th., Meth. and Appl., (5) 27 (1996), 589-603.
13. +, Proc. Am. Math. Soc., Vol., (2) 128 (2000), 439-444.
14. [Ko2] M.K. Korten, On the rectifiability of the free boundary of the one phase Stefan problem, Comm. in Analysis and Geom., (2) 13 (2005), 363-379.
15. [KoMo] M.K. Korten and C.N. Moore, On the free boundary of the two phase Stefan problem under minimal assumptions, submitted.
16. [Ma] P. Mattila, "Geometry of sets and measures in euclidean spaces", Cambridge studies in advanced mathematics 44, Cambridge University Press 1995.
17. [Wel] G. Weiss, Partial regularity for a minimum problem with free boundary, Journal Geom. Anal., 9 (1999), 317-326.
18. [We2] G. Weiss, A singular limit arising in combustion theory: fine properties of the free boundary, Calc. Var., 17 (2003), 311-340.