Chicco, Maurizio; Venturino, Marina A priori inequalities in \(L^\infty (\Omega)\) for solutions of elliptic equations in unbounded domains. (English) Zbl 0949.35044 Rend. Semin. Mat. Univ. Padova 102, 141-149 (1999). Summary: We prove some a priori inequalities in \(L^\infty(\Omega)\) for subsolutions of elliptic equations in divergence form, with Dirichlet’s boundary conditions, in unbounded domains. Cited in 2 Documents MSC: 35J25 Boundary value problems for second-order elliptic equations 35B45 A priori estimates in context of PDEs 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:subsolutions; Dirichlet’s boundary conditions; unbounded domains PDFBibTeX XMLCite \textit{M. Chicco} and \textit{M. Venturino}, Rend. Semin. Mat. Univ. Padova 102, 141--149 (1999; Zbl 0949.35044) Full Text: Numdam EuDML References: [1] H. Brézis - P. L. LIONS, An estimate related to the strong maximum principle , Boll. Un. Mat. Ital. ( 5 ), 17-A ( 1980 ), pp. 503 - 508 . MR 590969 | Zbl 0436.35016 · Zbl 0436.35016 [2] C. Miranda , Alcune osservazioni sulla maggiorazione in Lv delle soluzioni deboli delle equazioni ellittiche del secondo ordine , Ann. Mat. Pura Appl. ( 4 ), 61 ( 1963 ), pp. 151 - 170 . MR 177187 | Zbl 0134.09102 · Zbl 0134.09102 · doi:10.1007/BF02412852 [3] G. Stampacchia , Le problème de Dirichlet pour les équations elliptiques du second ordre d coefficients discontinus , Ann. Inst. Fourier ( Grenoble ), 15 ( 1965 ), pp. 189 - 258 . Numdam | MR 192177 | Zbl 0151.15401 · Zbl 0151.15401 · doi:10.5802/aif.204 [4] G. Talenti , Best constant in Sobolev inequality , Ann. Mat. Pura Appl. ( 4 ), 110 ( 1976 ), pp. 353 - 372 . MR 463908 | Zbl 0353.46018 · Zbl 0353.46018 · doi:10.1007/BF02418013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.