Abstract Let θ=(θ 0, θ 1) be a fixed vector in R 2 with strictly positive components and
suppose σ 0, σ 1> 0. Set σ θ= θ 0 σ 0+ θ 1 σ 1 and, if x 0, x 1∈ R n, set x θ= θ 0 x 0+ θ 1 x 1 …

This textbook originated from the teaching experience of the first author at the Scuola
Normale Superiore, where a course on optimal transport and its applications has been given …

This paper is devoted to one-dimensional interpolation Gagliardo–Nirenberg–Sobolev
inequalities. We study how various notions of duality, transport and monotonicity of …

To write anything in honour of SERRIN is a more than ordinary challenge to one who cannot
claim to be fully a mathematician. The writ of rigour and the canons of elegance, which must …

Let Ω, Γ, v, a and X be as described at the beginning of the introduction below, let p∈]
1,+∞[, and set q= p/(p-1). If p> 2, we also assume that the mean curvature {itx}{su (itx)} of Γ is …

These notes record the six lectures for the CIME Summer Course held by the second author
in Cetraro during the week of June 23–28, 2008, with minor modifications. Their goal is to …

The usual optimal transport (for the quadratic cost c (z)=| z| 2/2) characterized by Brenier [2]
as the gradient of a convex function is a very useful tool in geometric analysis for proving …

Equivalence of Dimension-Free Harnack Inequality and Curvature Condition Page 1 Integr. equ.
oper. theory 48 (2004), 547–552 0378-620X/040547-6, DOI 10.1007/s00020-002-1264-y c© …

Introduction. In [3] Nirenberg has proved maximum principles, both weak and strong, for
parabolic equations. In § 1 of this paper we give a generalization of his strong maximum …

A Generalized Diffusion Equation: Radial Symmetries and Comparison Theorems Page 1
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 95. 37-68 (1983) A …