Giorgio Talenti

TL;DR: In this paper, it was shown that if a positive absolutely continous measure causes a special relative isoperimetric inequality to hold, then Dirichlet-type integrals of sufficiently smooth real-valued functions decrease under an appropriate equimeasurable rearrangement.

TL;DR: In this article, the development of a relevant theory over the years and some applications to mathematical analysis, calculus of variations and partial differential equations are surveyed, as well as the applications of such a theory to realvalued functions of one or more real variables.

TL;DR: In this paper, the authors consider a Young function and assume that the distributional derivatives of the Young function satisfy the following properties: the support of u is bounded, u is real-valued, and u is locally integrable in euclidean n-dimensional space R n.

TL;DR: The existence of the real part of solutions, which need not be smooth, is derived in the present paper, where qualitative properties of smooth solutions are offered.

TL;DR: The following equation and related partial differential equations and systems, which arise in a generalization of geometrical optics, are investigated from a theoretical point of view in this article, where qualitative properties of smooth solutions are derived.