References
Alikakos, N.D.: An application of the invariance principle to reaction-diffusion equations. J. Differential Equations33, 201–225 (1979)
Alikakos, N.D.:L p bounds of solutions of reaction-diffusion equations. Comm. Partial Differential Equations4, 827–868 (1979)
Alikakos, N.D., Rostamian, R.: Large time behavior of solutions of Neumann boundary value problem for the porous medium equation. Indian Univ. Math. J.30, 749–785 (1981)
Aronson, D.G., Serrin, J.: A maximum principle for nonlinear parabolic equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci.21, 291–305 (1967)
Aronson, D.G., Peletier, L.A.: Large time behavior of solutions of the porous medium equation in bounded domains. J. Differential Equations39, 378–412 (1981)
Attouch, H., Damlamian, A.: Application des methodes de convexité et monotonie a l'étude de certaines equations quasi-lineaires. Proc. Royal Soc. Edinburgh Sect. A79, 107–129 (1977)
Brezis, H.: One some degenerate nonlinear parabolic equations. Proc. Symp. Pure Math. Vol. 18. Providence, R. I. A.M.S. 1970
Casten, R.G., Holland, C.J.: Instability results for reaction-diffusion equations with Neumann boundary conditions. J. Differential Equations27, 266–273 (1978).
Crandall, M.G., Benilan, Ph.: Regularizing effects of homogeneous evolution equations (preprint)
Evans, L.C.: Application of nonlinear semigroup theory to certain partial differential equations. In: nonlinear evolution equations. Crandall, M.G., ed. New York: Academic Press 1978.
Evans, L.C.: Regularity properties for the heat equation subject to nonlinear boundary constraints. J. Nonlinear Anal.1, 593–602 (1977)
Ladyzenskaja, O.A., Sollonnikov, V.A., Ural'ceva, N.N.: Linear and quasilinear equations of parabolic type. Moscow: Nauka 1967; English Transl. Math. Monographs, Vol. 23. Providence, R.I.: A.M.S. 1968
Lions, J.L.: Quelques méthode de résolution des problémes aux limites non linéaires. Paris: Dunod. 1969
Lions, J.L., Magenes, E.: Non-homogeneous boundary value problems and applications. Vol. 1. Berlin, Heidelberg, New York, Springer 1972
Moser, J.: A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations. Comm. Pure Appl. Math.13, 457–468 (1960).
Peletier, L.A.: The porous media equation. In: Applications of nonlinear analysis in the physical sciences, ed. Amann, H. et al. London: Pitman 1981
Simon, J.: Regularité de solutions de problémes non lineaires. C. R. Acad. Sci. Paris282, 947–950 (1976)
Temam, R.: On the Euler equations of incompressible perfect fluids. J. Functional Analysis20, 32–43 (1977)
Véron, L.: Coercitive et proprietes regularisantes des semi-groupes non lineaires dans les espaces de Banach. Publications Mathimatiques de Besancon (1977)
Vishik, I.M.: On the solutions of boundary value problems for quasilinear parabolic equations of arbitrary order. Math. USSR-Sb.59, 289–325 (1962) (in Russian)
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This research was supported in part by the National Science Foundation under Grant # MCS-8002540
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Alikakos, N.D., Rostamian, R. Gradient estimates for degenerate diffusion equations. I. Math. Ann. 259, 53–70 (1982). https://doi.org/10.1007/BF01456828
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DOI: https://doi.org/10.1007/BF01456828