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THE GEOMETRY OF SOME NONLINEAR PDES 133
E. DiBenedetto, J. M. Urbano and V. Vespri, Current issues on singular and degenerate evolution equations, in: Handbook of Differential Equations, Elsevier, to appear.
E. DiBenedetto and V. Vespri, On the singular equation β(u)t = ∆u, Arch. Ration. Mech. Anal. 132 (1995), 247-309.
E. Henriques and J. M. Urbano, On the doubly singular equation γ(u)t = ∆pu, Preprint no. 04-07, DMUC, Coimbra (http://www.mat.uc.pt/preprints/ps/p0407.pdf), submitted.
S. N. Kruˇzkov, An a priori estimate of the solutions of linear parabolic equations and solutions of boundary-value problems for a certain class of quasi-linear parabolic equations, Dokl. Akad. Nauk SSSR 138 (1961), 1005-1008. English Transl. in Soviet Math. Doklady 2 (1961), 764- 767.
, A priori bounds and some properties of solutions of elliptic and parabolic equations, Mat. Sb. (N.S.) 65 (107) (1964), 522-570 (Russian). Engl. Transl. in Amer. Math. Soc. Transl. 2 (68) (1968), 169-220.
O. A. Ladyzhenskaja and N. N. Ural’ceva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.
O. A. Ladyzhenskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and Quasilinear Equa- tions of Parabolic Type, AMS Transl. Math. Mono, Vol. 23, Providence RI, USA, 1968.
J. Moser, A new proof of DeGiorgi’s theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math. 13 (1960), 457-468.
, On Harnack’s theorem for elliptic differential equations, Comm. Pure Appl. Math. 14 (1961), 577-591.
, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101-134.
J. Nash, Continuity of solutions of parabolic and elliptic equations, Amer. J. Math. 80 (1958), 931-954.
J. Serrin, Local behaviour of solutions of quasilinear elliptic equations, Acta Math. 111 (1964), 101-134.
N. S. Trudinger, On Harnack type inequalities and their application to quasilinear elliptic partial differential equations, Comm. Pure Appl. Math. 20 (1967), 721-747.
, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 205-226.
J. M. Urbano, Continuous solutions for a degenerate free boundary problem, Ann. Mat. Pura Appl. (4) 178 (2000), 195-224.
Jose´ Miguel Urbano, Departamento de Matema´tica, Universidade de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal
E-mail address: jmurb@mat.uc.pt