Matemática

Working with singularities

Por Herwig Hauser (Fakultät für Mathematik, Universität Wien).

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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.

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The Cauchy-Dirichlet problem for impulsive ultra-parabolic equations

Por Ivan Kuznetsov (Lavrentyev Institute of Hydrodynamics – Siberian Division of the Russian Academy of Sciences, Novosibirsk State University).

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Optimal shape and location of actuators or sensors in PDE models

Por Yannick Privat (Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie).

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Algebraic and Analytic Aspects of Power Series

Numerous exciting results circle around the quality of specific power series: formal, convergent, algebraic, Gevrey, Mahler, D-finite, P-recursive, differentially algebraic, holonomic, hypergeometric, lacunary, G-functions, ..., with often sharp contrasts between characteristic zero and positive characteristic.

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A Matemática, associada a métodos subtis e engenhosos, permite fazer descobertas inesperadas e, porvezes, surpreendentes. Iremos aqui passar em revista algumas investigações feitas por este mundo fora, tentando perceber os seus resultados e lançar um olhar crítico sobre as conclusões que daí se podem tirar.