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Original Articles

Hölder estimates of solutions to some doubly nonlinear degenerate parabolic equations

Pages 895-913 | Published online: 08 May 2007

References

  • Alikakos and Evans , L.C. 1983 . Continuity of the gradient for weak solutions of a degenerate parabolic equation . J. Math. Pures Appl. , 62 : 253 – 268 .
  • Alikakos , N.D. and Rostmian , R. 1982 . Gradient estimates for degenerate diffusion equations II . Proc. Roy. Soc. Edinburgh , 91A : 335 – 346 .
  • Ames , W.F. 1965 . “ Nonlinear Partial Differential Equations in Engineering ” . Vol. I , New York : Academic Press .
  • Aronson , D.G. 1969 . Regularity properties of flows through porous media . SIAM J. Appl. Math. , 17 : 461 – 467 .
  • Aronson , D.G. 1985 . “ The Porous Medium Equation ” . In Lecture Notes in Mathematics , Vol. 1224 , Springer Verlag .
  • Benilan , P. 1983 . A Strong regularity Lp for solutions of the porous media equation . Research Notes Math. Pitman, London , 89 : 39 – 58 .
  • Caffarelli , L.A. and Friedman , A. 1979 . Continuity of the density of a gas flow in a porous medium . Tran. Amer. Math. Soc. , 252 : 99 – 113 .
  • Caffarelli , L.A. , Vazquez , J.L. and Wolanski , N.I. 1987 . Lipschitzcontinuity of solutions and interfaces of teh N—dimensional porous medium equation . Indiana Univ. Math. J. , 36 : 373 – 401 .
  • Chen , Yazhe and DiBenedetto , E. 1992 . Hölder estimates of solutions of singular parabolic equations with measurable coefficients . Arch. Rat. Mech. Anal. , 118 : 257 – 271 .
  • Chen , Yazhe . 1984 . Hölder estimates for solutions of uniformly degenerate quasi—linear parabolic equations . Chin. Ann. Math. , 5 : 661 – 678 .
  • Dibenedetto , E. 1993 . “ Degenerate Parabolic Equations ” . Springer Verlag .
  • DiBenedetto , E. and Friedman , A. 1985 . Hölder estimates for nonlinear degenerate parabolic systems . J. Reine Angew. Math. , 357 : 1 – 22 .
  • Esteban , J.r. and Vazquez , J.L. 1986 . On the equation of Turbulent filtration in one—dimensional porous media . Nonlinear Analysis, TMA. , 10 : 1303 – 1325 .
  • Gilding , B.H. 1976 . Hölder continuity of solutions of parabolic equations . J. London Math. Soc. , 13 : 103 – 106 .
  • Gilding , B.H. and Peletier , L.A. 1981 . Continuity of solutions of the porous media equations . Ann. Scuola Norm. Sup. Pisa , 8 : 659 – 675 .
  • Gurtin , M.E. and MacCamy , R.C. 1977 . On the diffusion of bilogical population . Math. Biosc. , 33 : 35 – 49 .
  • Herrero , M.A. and Pierre , M. 1985 . The cauchy rpoblem for . Trans. Amer. math. Soc. , 281 : 145 – 158 .
  • Jäger , W. and Lu , Y.G. 1997 . Global regularity of solutions for general degenerate parabolic equations in 1—D . J. Diff. Equs. , 140 : 365 – 377 .
  • W. Jäger and Y.G. Lu, Hölder continuity of solutions of degenerate parabolic equations, to appear.
  • Kalashnikov , A.S. 1987 . Some problems of the qualitative theory of non—linear degenerate second—order parabolic equations . Rusian Math. Surveys , 42 : 169 – 222 .
  • Ladyzhenskaya , O.A. 1967 . New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems form them, English transl . Trudy Math. Inst. Steklov , 102 : 85 – 104 .
  • W. Jäger and Y.G. Lu, Hölder continuity of solutions of degenerate parabolic equations, to appear. Y.G. Lu, Hölder Estimates of Solutions of Biological Population Equations, to appear.
  • Oleinik , O.A. , Kalashnikov , A.S. and Chzou , Yui—lin . 1958 . The Cauchy problem and boundary problems for equations of the type of unsteady filtration . Izvestya Akademii Nauk SSR Serija math emaicheskaja , 22 : 667 – 704 .
  • Porzio , M.M. and Vespri , V. 1993 . Hölder estimates for local solutions of some doubly nonlinear degenerate parabolic equations . J. Diff. Eqns. , 103 : 146 – 178 .
  • Serrin , J. 1959 . “ Mathematical principles of classical fluid mechanics ” . In In Handbuch der Physik , Edited by: Flügge , S . Vol. III/1 , Berlin: Springer .
  • Smoller , J.A. 1982 . “ Shock Waves and Reaction—Diffusion Equations ” . New York, , Berlin : Springer Verlag .
  • Vespri , V. 1992 . On the local behavior of solutions of a certain class of doubly nonlinear parabolic equations . Manuscripta Mathematica , 75 : 65 – 80 .
  • Ziemer , W.P. 1982 . Interior and boundary continuity of weak solutions of degenerate parabolic equations . Tran. AMS , 271 : 733 – 748 .
  • Kilpeläinen , T. and Lindqvist , P. 1996 . On the Dirichlet boundary value problem for a degenerate parabolic equation . SIAM J. Math. Anal. , 27 : 661 – 683 .

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