Nonlinear differential equations, Lect. 7th Congr., Granada/Spain 1984, Res. Notes Math. 132, 155-181 (1985).
[For the entire collection see Zbl 0638.00015.]
Consider a nonlinear elliptic equation of the type
where is a regular bounded open set of R N, L is a linear elliptic second order operator
(1) appears in many different contexts: in the study of isothermal chemical reactions, of stationary solutions of many nonlinear evolution equations, and others. Many authors considered the existence and properties of a free boundary F(u) for solutions of (1). The author in this paper obtains some qualitative properties in F(u) using symmetric rearrangement of a function in the sense of Hardy and Littlewood.