Kesavan, S.; Pacella, Filomena Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities. (English) Zbl 0833.35040 Appl. Anal. 54, No. 1-2, 27-37 (1994). It is proved that positive solutions of nonlinear equations involving the \(N\)-Laplacian in a ball in \(\mathbb{R}^N\) with Dirichlet boundary conditions are radial and radially decreasing provided that the nonlinearity is a continuous function \(f(t)\) (satisfying suitable growth conditions) which is strictly positive for \(t> 0\). The method generalizes that of Lions for the Laplacian in two dimensions. The method of the present paper can also be extended to an analogous mixed boundary value problem in a convex cone. Reviewer: S.Kesavan (Bangalore) Cited in 22 Documents MSC: 35J60 Nonlinear elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:radial symmetric solution; mixed boundary value problem in a convex cone PDFBibTeX XMLCite \textit{S. Kesavan} and \textit{F. Pacella}, Appl. Anal. 54, No. 1--2, 27--37 (1994; Zbl 0833.35040) Full Text: DOI References: [1] Adimurthi, Elementary proof for the uniqueness of positive radial solution of a semilinear Dirichlet problem, Preprint (1992) [2] Badiale M., A note on the radiality of solutions of p–Laplacian equation, Preprint (1992) · Zbl 0841.35008 [3] DOI: 10.1007/BF01244896 · Zbl 0784.35025 · doi:10.1007/BF01244896 [4] DOI: 10.1016/0022-1236(89)90007-4 · Zbl 0706.35021 · doi:10.1016/0022-1236(89)90007-4 [5] Brothers J., J. Reine Angew Math. 384 pp 153– (1988) [6] DOI: 10.1007/BF01221125 · Zbl 0425.35020 · doi:10.1007/BF01221125 [7] DOI: 10.1016/0362-546X(89)90020-5 · Zbl 0714.35032 · doi:10.1016/0362-546X(89)90020-5 [8] DOI: 10.1088/0951-7715/3/3/008 · Zbl 0719.35027 · doi:10.1088/0951-7715/3/3/008 [9] DOI: 10.1080/00036818108839367 · Zbl 0445.35043 · doi:10.1080/00036818108839367 [10] DOI: 10.1090/S0002-9939-1990-1000160-1 · doi:10.1090/S0002-9939-1990-1000160-1 [11] Mossino J., Inégalités Isopérimétriques et Application en Physique (1984) [12] Pacella F., Progress in NOnlinear Differential Equations 4 (1990) · Zbl 0725.52007 [13] Pohozaev S., Soviet Math. Dokl. 6 pp 1408– (1965) [14] Talenti G., Annali Scuola Norm. Sup. di Pisa 4 pp 697– (1976) 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.