Rearrangements and convexity of level sets in PDE
The first part of this work is a survey on rearrangement technique and its applications to partial differential equations and the calculus of variations. The author studies in detail the main types of rearrangements for functions of one and several variables and uses the general theory to prove convexity or symmetry properties of solutions of differential equations. The applications include the treatment of some free boundary problems such as the dam problem, the capacitary problem, the theory of jets and cavities. The second part of the book concerns the applications of the maximum principle to obtain the same type of results. The work contains several original contributions of the author and solves many interesting problems and conjectures on the shape of free boundary of elliptic variational inequalities.
scientific article; zbMATH DE number 3953325