$L^{\infty }$-estimates for nonlinear parabolic equations with natural growth conditions

 Access to full text

 Full (PDF)

1. [1] A. Alvino - P.L. Lions - G. Trombetti, Comparison results for elliptic and parabolic equations via Schwartz symmetrisation, Ann. Inst. Herni Poincarè, Analyse non lineaire, to appear. Zbl0703.35007MR1051227
2. [2] L. Boccardo - F. Murat - J.P. Puel, Existence de solutions faible pour des equations elliptiques quasi lineaires a croissance quadratique, Research Notes in Mathematics, 84, Pitman, London (1983), pp. 19-73. Zbl0588.35041MR716511
3. [3] L. Boccardo - F. Murat - J.P. Puel, Resultats d'existence pour certains problemes quasi lineaires, Ann. Sc. Norm. Sup. Pisa, 11 (1984), pp. 213-235. Zbl0557.35051MR764943
4. [4] L. Boccardo - F. Murat - J.P. Puel, Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl., 152 (1988), pp. 183-196. Zbl0687.35042MR980979
5. [5] L. Boccardo - F. Murat - J.P. Puel, Quelques proprietes des operateurs elliptiques quasi lineaires, C.R.A.S., 307, Serie I (1988), pp. 749-752. Zbl0696.35050MR972073
6. [6] L. Boccardo - F. Murat - J.P. Puel, Existence results for some quasilinear parabolic equations, NonLinear Anal., 13 (1989), pp. 373-392. Zbl0705.35066MR987375
7. [7] L. Boccardo - F. Murat - J.P. Puel, L∞ estimate for some nonlinear elliptic partial differential equation and application to an existence result, SIAM J. Math. Anal., to appear. Zbl0785.35033
8. [8] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies, Princeton, N.Y. (1983). Zbl0516.49003MR717034
9. [9] A. Ladyzhenskaja - V. A. SOLONNIKOV - N. N. URAL'CEVA, Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Transl., Providence, R. I. (1968). Zbl0174.15403
10. [10] C. Maderna - S. SALSA, Dirichlet problem for elliptic equations with nonlinera first order term: a comparison result, Ann. Mat. Pura Appl., 148 (1987), pp. 277-288. Zbl0657.35053MR932768
11. [11] L. Orsina - M.M. Porzio, L∞ (Ω) estimate and existence of solutions for some nonlinear parabolic equations, B.U.M.I., to appear. Zbl0783.35026
12. [12] G. Stampacchia, Le probleme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus, Ann. Inst. Fourier, 15 (1965), pp. 189-258. Zbl0151.15401MR192177
13. [13] G. Stampacchia, Equation elliptiques du second ordre a coefficients discontinus, Séminaires de Mathématiques Supérieures, 16, Les presses de l 'Université de Montreal, Montreal (1966). Zbl0151.15501MR251373