Maximal regularity for a free boundary problem

Joachim Escher1, Gieri Simonett2
1Institute of Mathematics, University of Basel, Basel, Switzerland
2Department of Mathematics, Vanderbilt University, Nashville, U.S.A.

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S. AGMON, A. DOUGLIS, L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I,Comm. Pure Appl. Math. 12, 623?727 (1959)

H. AMANN, Existence and regularity for semilinear parabolic evolution equations,Ann. Scuola Norm. Pisa, (4) XI, 593?676 (1984).

H. AMANN, Dynamic theory of quasilinear parabolic equations. I.Nonlinear Anal., TMA 12, 895?919 (1988)

H. AMANNLinear and Quasilinear Parabolic Problems, Book in preparation, 1994

H. AMANN, J. ESCHER, Strongly continuous dual semigroups, to appear inAnn. Mat. Pura Appl.

S. B. ANGENENT, Nonlinear analytic semiflows,Proc. Roy. Soc. Edinburgh 115 A, 91?107 (1990)

J. BEAR, Y. BACHMAT,Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer Academic Publisher, Boston, 1990

F. E. BROWDER, On the spectral theory of elliptic operators I,Math. Ann. 142, 22?130 (1961)

G. DA PRATO, P. GRISVARD, Equations d'�volution abstraites nonlin�aires de type parabolique,Ann. Mat. Pura Appl., (4) 120, 329?396 (1979)

C. M. ELLIOTT, J. R. OCKENDON,Weak and Variational Methods for Moving Boundary Problems, Pitman, Boston, 1982

J. ESCHER, Nonlinear elliptic systems with dynamic boundary conditions,Math. Z. 210, 413?439 (1992)

J. ESCHER, The Dirichlet-Neumann operator on continuous functions,Ann. Scuola Norm. Pisa, (4) XXI, 235?266 (1994)

A. FRIEDMAN, B. HU, The Stefan problem with kinetic condition at the free boundary,Ann. Scuola Norm. Pisa, (4) XLIV, 87?111 (1992)

D. GILBARG, N.S. TRUDINGER,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977

G. GRUBB,Functional Calculus of Pseudo-Differential Boundary Problems, Birkh�user-Verlag, Basel, 1986

T. HINTERMANN, Evolution equations with dynamic boundary conditions,Proc. Roy. Soc. Edinburgh 113 A, 43?60 (1989)

B. HUNT, Vertical recharge of unconfined aquifer.J. Hydr. Divn. 97, 1017?1030 (1971)

A. LUNARDI. On the local dynamical system associated to a fully nonlinear abstract parabolic equation. InNonl. Anal. and Appl., ed. Lakshmikantham, M. Dekker, New York, 319?326 (1987)

A. LUNARDI, Analyticity of the maximal solution of an abstract nonlinear parabolic equation,Nonlinear Anal. TMA,6, 503?521 (1982)

A. LUNARDI,Analytic Semigroups and Optimal Regularity in Parabolic Equations, Birkh�user-Verlag, Basel, 1994

H. KAWARADA, H. KOSHIGOE, Unsteady flow in porous media with a free surface,Japan J. Indust. Appl. Math.,8, 41?82 (1991)

B. E. PETERSON,Introduction to Fourier Transform and Pseudo-Differential Operators, Pitman, Boston, London, 1983

M. H. PROTTER, H. F. WEINBERGER,Maximum Principles in Differential Equations, Springer-Verlag, Berlin, 1984

G. SIMONETT, Zentrumsmannigfaltigkeiten f�r quasilineare parabolische Gleichungen.Institut f�r angewandte Analysis und Stochastik, Report Nr. 2, Berlin, 1992

G. SIMONETT, Quasilinear parabolic equations and semiflows. InEvolution Equations, Control Theory, and Biomathematics, Lecture Notes in Pure and Appl. Math. M. Dekker, New York, 523?536 (1994)

E. SINESTRARI, Continuous interpolation spaces and spatial regularity in nonlinear Volterra integrodifferential equations,J. Integral Equs. 5, 287?308 (1983)

E. M. STEIN,Singular Integrals and Differentiability Properties of Functions, University Press, Princeton, 1970

H. TRIEBEL,Theory of Function Spaces, Birkh�user-Verlag, Basel, 1983

H. TRIEBEL,Theory of Function Spaces II, Birkh�user-Verlag, Basel, 1992