Article PDF
References
P. Bénilan -L. Boccardo -T. Gallouët -R. Gakiepy -M. Pierre-J. L. Vazquez,An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa,22, n. 2 (1995), pp. 240–273.
A.Bensoussan - L.Boccardo - A.Dall'Aglio - F.Murat,H-convergence of quasi-linear elliptic equations under natural hypotheses on the correctors, onComposite Media and Homogenization Theory (Trieste, 1993), edited by G.Dal Maso and G.Dell'Antonio, Birkhaüser, to appear.
A. Bensoussan -L. Boccardo -F. Murat,H-convergence for quasi-linear elliptic equations with quadratic growth, Appl. Math. Optim.,26 (1992), pp. 253–272.
A. Bensoussan -J. L. Lions -G. Papanicolau,Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam (1978).
M. Biroli,Existence et estimations de type Meyers pour les problèmes d'obstacle paraboliques quasi linéaires, C. R. Acad. Sc. Paris,303, Série I 12 (1986), pp. 543–545.
D.Blanchard - F.Murat,Renormalized solutions of nonlinear parabolic problems with L1 data: existence and uniqueness, to appear.
L. Boccardo -T. Del Vecchio,Homogenization of strongly nonlinear equations with gradient dependent lower order nonlinearity, Asymp. Anal.,5 (1991), pp. 75–90.
L. Boccardo -T. Gallouët,Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal.,87 (1989), pp. 149–169.
L.Boccardo - F.Murat,Homogénéisation de problèmes quasi-linéaires, inAtti del Convegno «Studio di problemi limite dell'Analisi Funzionale», Bressanone 7–9 settembre 1981, Pitagora ed. (1982), pp. 13–51.
L. Boccardo -F. Murat,Strongly nonlinear Cauchy problems with gradient dependent lower order non-linearity, inRecent Advances in Nonlinear Elliptic and Parabolic Problems (Proceedings, Nancy 1988), edited byP. Benilan,M. Chipot,L. C. Evans andM. Pierre, Pitman Research Notes in Mathematics Series, Longman, Harlow (1989), pp. 247–254.
L. Boccardo -F. Murat -J. P. Puel,Existence results for some quasilinear parabolic equations, Nonlinear Anal.,13 (1989), pp. 373–392.
S.Brahim-Otsmane - G.Francfort - F.Murat,Correctors for the homogenization of the wave and heat equations, J. Math. Pures Appl., to appear.
F. Colombini -S. Spagnolo,Sur la convergence de solutions d'équations paraboliques, J. Math. Pures Appl.,56 (1977), pp. 263–306.
A.Dall'Aglio,Alcuni problemi relativi alla H-convergenza di equazioni ellittiche e paraboliche quasilineari, Tesi di Dottorato in Matematica, Università di Roma (1992).
M. Giaquinta -M. Struwe,On the partial regularity of weak solutions of parabolic systems, Math. Zeit.,179 (1982), pp. 437–451.
N.Grenon,Résultats d'existence et de comportement asymptotique pour des équations paraboliques quasilinéaires, These de doctorat, Université d'Orleans.
O. Ladyzhenskaya -V. Solonnikov -N. Uralceva,Linear and Quasilinear Equations of Parabolic Type, Trans. of Math. Monographs, Vol.23, A.M.S., Providence (1968).
J. L. Lions,Quelques méthodes de resolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris (1969).
P. L.Lions - F.Murat, to appear.
N. G. Meyers,An Lp-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Sc. Norm. Sup. Pisa,17 (1963), pp. 189–200.
A. Mokrane,Existence of bounded solutions for some nonlinear parabolic equations, Proc. Roy. Soc. Edinburgh, Sect. A,107 (1987), pp. 313–326.
F.Murat,Equations elliptiques non linéaires avec second membre Lp ou mesure, Actes du 26ème Congrès National d'Analyse Numérique (Les Karellis, 1994), to appear.
L.Tartar,Cours Peccot, Collège de France, March 1977. Partially written in F.Murat,H-convergence, Séminaire d'Analyse Fonctionnelle de l'Université d'Alger, 1977–78. English translation inMathematical Modeling of Composite Materials, edited by R. V.Kohn;Progress in Nonlinear Differential Equations and their Applications, Birkhäuser, Boston (1994).
L. Orsina -M. M. Porzio,L ∞ (Q)-estimate and existence of solutions for some nonlinear parabolic equations}, Boll. Un. Mat. Ital.,6-A (1992), pp. 631–647.
A. Prignet,Remarks on existence and uniqueness of solutions of elliptic problems with right-hand side measures, Rend. Mat.,15 (1995), pp. 321–337.
E.Sanchez-Palencia,Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics,127, Springer.
J.Serrin,Pathological solutions of elliptic differential equations, Ann. Sc. Norm. Sup. Pisa (1964), pp. 385–387.
J. Simon,Compact sets in the space Lp(O, T; B), Ann. Mat. Pura Appl.,146 (1987), pp. 65–96.
S. Spagnolo,Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore, Ann. Sc. Norm. Sup. Pisa,21 (1967), pp. 657–699.
S. Spagnolo,Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche, Ann. Sc. Norm. Sup. Pisa,22 (1968), pp. 577–597.
S. Spagnolo,Convergence of parabolic equations, Boll. Un. Mat. Ital.,14-B (1977), pp. 547–568.
G. Stampacchia,Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier, Grenoble,15 (1965), pp. 189–258.
V. V. Zhikov -S. M. Kozlov -O. A. Oleinik,G-convergence of parabolic operators, Russian Math. Surveys,361, 1 (1981), pp. 9–60.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dall'Aglio, A. Approximated solutions of equations withL 1 data. Application to theH-convergence of quasi-linear parabolic equations. Annali di Matematica pura ed applicata 170, 207–240 (1996). https://doi.org/10.1007/BF01758989
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01758989