Alvino, Angelo; Lions, Pierre-Louis; Trombetti, Guido Comparaison des solutions d’équations paraboliques et elliptiques par symétrisation. Le cas de la symétrisation de Schwarz. (Comparison results for solutions of parabolic and elliptic equations via symmetrization. The case of Schwarz symmetrization). (French) Zbl 0602.35008 C. R. Acad. Sci., Paris, Sér. I 303, 947-950 (1986). We study the comparison of solutions of parabolic and elliptic equations with solutions of an adequate symmetrized problem. In the case of Schwarz symmetrization, we give a general result and indicate some counter- examples; we also consider the case of quasilinear equations. Cited in 2 Reviews MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs 35G20 Nonlinear higher-order PDEs Keywords:comparison; symmetrized problem; Schwarz symmetrization; quasilinear equations PDFBibTeX XMLCite \textit{A. Alvino} et al., C. R. Acad. Sci., Paris, Sér. I 303, 947--950 (1986; Zbl 0602.35008)