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Keywords:
maximum principle; weak subsolution; degenerate equation
maximum principle; weak subsolution; degenerate equation
Summary:
Sufficient conditions are obtained so that a weak subsolution of $(0.1)$, bounded from above on the parabolic boundary of the cylinder $Q$, turns out to be bounded from above in $Q$.
References:
[1] Bonafede S.: Sottosoluzioni deboli delle equazioni paraboliche lineari del secondo ordine degeneri. Rendiconti del circolo Matematico di Palermo, Serie II, Tomo XXXIX (1990), 132-152.
[2] Eklund N.A.: Generalized super-solution of parabolic equations. Transaction of the American Mathematical Society 220 (1976), 235-242. MR 0473522
[3] Gagliardo E.: Proprieta' di alcune classi di funzioni in piu' variabili. Ricerche di Matematica 7 (1958), 102-137. MR 0102740 | Zbl 0089.09401
[4] Ivanov A.V.: Properties of solutions of linear and quasilinear second-order equations with measurable coefficients which are neither strictly nor non uniformly parabolic. Zap. Nauch. Sem. Leningrad Otdel Mat. Inst. Steklov (LOMI) 69 (1977), 45-65 Transl. in Journal of Soviet Math., 10 (1978), pp. 29-43. MR 0603301
[5] Ladyzhenskaya O.A., Ural'tseva N.N.: Linear and quasilinear elliptic equations. Academic Press, New York, 1968. MR 0244627 | Zbl 0177.37404
[6] Nicolosi F.: Sottosoluzioni deboli delle equazioni paraboliche lineari del secondo ordine superiormente limitate. Le Matematiche 28 (1973), 361-378. MR 0364867
[7] Nicolosi F.: Soluzioni deboli dei problemi al contorno per operatori parabolici che possono degenerare. Annali di Matematica (4) 125 (1980), 135-155. MR 1553443 | Zbl 0452.35065
[8] Stampacchia G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Annal. Inst. Fourier 15 (1965), 189-257. MR 0192177 | Zbl 0151.15401
[9] Troianello G.M.: On weak subsolutions for parabolic second-order operators. Comm. in Partial Diff. Equat. 3 (10), 933-948. MR 0507123
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