A HELE-SHAW problem for tumor growth

Caffarelli, L. A. The regularity of free boundaries in higher dimensions . Acta Math. 139 (1977), no. 3-4, 155–184

1977

Earlier work this paper cites.

Aronson, D. G.; Bénilan, Ph. Régularité des solutions de l’équation des milieux poreux dans R N R^{N} . C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 2, A103–A105

1979

Earlier work this paper cites.

Caffarelli, L. A. A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets . Boll. Un. Mat. Ital. A 18 (1981), no. 1, 109–113

1981

Earlier work this paper cites.

Elliot, C. M.; Janovský, V. A variational inequality approach to Hele-Shaw flow with a moving boundary . Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), no. 1–2, 93–107

1981

Earlier work this paper cites.

Matano, H. Asymptotic behavior of the free boundaries arising in one-phase Stefan problems in multidimensional spaces . Nonlinear partial differential equations in applied science (Tokyo, 1982), 133–151, North-Holland Math. Stud., 81, North-Holland, Amsterdam, 1983

1983

Earlier work this paper cites.

Giusti, E. Minimal surfaces and functions of bounded variation . Monographs in Mathematics, 80. Birkhäuser Verlag, Basel, 1984

1984

Earlier work this paper cites.

Caffarelli, L. A.; Vázquez, J. L.; Wolanski, N. I. Lipschitz continuity of solutions and interfaces of the N -dimensional porous medium equation . Indiana Univ. Math. J. 36 (1987), no. 2, 373–401

1987

Cited alongside, same era.

Caffarelli, L. A. The obstacle problem revisited . J. Fourier Anal. Appl. 4 (1998), no. 4-5, 383–402

1998

Cited alongside, same era.

Blank, I. Sharp results for the regularity and stability of the free boundary in the obstacle problem . Indiana Univ. Math. J. 50 (2001), no. 3, 1077–1112

2001

Cited alongside, same era.

Gil, O.; Quirós, F. Convergence of the porous media equation to Hele-Shaw . Nonlinear Anal. Ser. A: Theory Methods 44 (2001), no. 8, 1111–1131

2001

Cited alongside, same era.

Gil, O.; Quirós, F. Boundary layer formation in the transition from the porous media equation to a Hele-Shaw flow . Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 1, 13–36

Kim, I. C.; Mellet, A. Homogenization of a Hele-Shaw problem in periodic and random media . Arch. Ration. Mech. Anal. 194 (2009), no. 2, 507–530

2009

Later among the works it cites.

T. Colin, D. Bresch, E. Grenier, B. Ribba and O. Saut,, Computational modeling of solid tumor growth: the avascular stage, SIAM Journal of Scientific Computing

2010

Later among the works it cites.

Lowengrub, J. S.; Frieboes H. B.; Jin, F.; Chuang, Y.-L.; Li, X.; Macklin, P.; Wise, S. M.; Cristini, V. Nonlinear modelling of cancer: bridging the gap between cells and tumours . Nonlinearity 23 (2010), no. 1, R1–R91

2010

Later among the works it cites.

Andersson, J.; Lindgren, E.; Shahgholian, H. Optimal regularity for the no-sign obstacle problem . Comm. Pure Appl. Math. 66 (2013), no. 2, 245–262

2013

Later among the works it cites.

Perthame, B.; Quirós, F.; Vázquez, J. L. The Hele-Shaw asymptotics for mechanical models of tumor growth . Arch. Ration. Mech. Anal. 212 (2014), no. 1, 93–127