Nonlinear Dirichlet Problems: Old and New

Por Lucio Boccardo (Dipartimento di Matematica, "Sapienza" Università di Roma).

Abstract: We present a review on the Stampacchia-Calderon-Zygmund theory for linear elliptic operators of second order with discontinuous coefficients and the corresponding theory for nonlinear operators of Leray-Lions type with nonregular data.

We shall also discuss classical and recent results, including work in progress, on the continuous dependence of the solutions with respect to right hand sides.

Fractionary powers of Laplacians in Fluid Mechanics

Por Antonio Córdoba (Universidad Autónoma de Madrid).

Abstract: Fractional powers of Laplacians play an important role in the evolution of fluid interphases and atmospheric fronts. There are several useful, and to some extend surprising, new pointwise inequalities satisfied by those operators which help us to understand the nature of several models in Fluid Mechanics, such as SQG, Hele-Shaw cells or Muskat’s problem.