Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface

@inproceedings{Choi2007RegularityFT,
  title={Regularity for the one-phase Hele-Shaw problem from a Lipschitz initial surface},
  author={H Choi},
  year={2007}
}
In this paper we show that if the Lipschitz constant of the initial free boundary is small, then for small positive time the solution is smooth and satisfies the Hele-Shaw equation in the classical sense. A key ingredient in the proof which is of independent interest is an estimate up to order of magnitude of the speed of the free boundary in terms of initial data. 0. Introduction. Consider a compact set K ⊂ Rn with smooth boundary ∂K. Suppose that a bounded domain Ω contains K and let Ω0… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 11 references

Uniqueness and Existence result of Hele-Shaw and Stefan problem, Arch

I. Kim
Rat. Mech. Anal • 2003

Regularity of the free boundary in parabolic phasetransition problems

ACS I. Athanasopoulos, L. Caffarelli, S. Salsa
Acta Math • 1996

Persistence of corners in free boundaries in Hele-Shaw flow, Euro

J. R. King, A. A. Lacey, J. L. Vazquez
J. Appl. Math • 1995

A Harnack inequality approach to the regularity of free boundaries, Part II: Flat free boundaries are Lipschitz, Comm

L. Caffarelli
Pure Appl. Math • 1989

A Harnack inequality approach to the regularity of free boundaries, Part I: Lipschitz free boundaries are C1,α

L. Caffarelli
Rev. Mat. Iberoamericana • 1987

Boundary behavior of Harmonic functions in Non-tangentially Accessible Domains

D. S. Jerison, C. E. Kenig
Adv. Math • 1982

A variational inequality approach to Hele-Shaw flow with a moving boundary

C. M. Elliot, V. Janovsky
Proc. Roy. Soc. Edinburgh Sect. A • 1981

Harmonic functions in Lipschitz domains, Harmonic analysis in Euclidean spaces

B. Dahlberg
Proc. Sympos. Pure Math., vol. XXXV, Part 1, Amer. Math. Soc., Providence, • 1979

Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform

R. Hunt, R. B. Muckenhoupt
Trans. Amer. Math. Soc • 1973

Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand

K.-O. Widman
1967

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