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M. Cinquini Cibrario: Equazioni non lineari e teoria delle caratteristiche.- J. Leray: La théorie de L. Garding des équations hyperboliques lineaires.- S.L. Sobolev: Lezioni sulle equazioni iperboliche non lineari.- A Weinstein: Equazioni alle derivate parziali singolari.

Partial differential equations --- differentiaalvergelijkingen

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J. Leray, J.L. Lions: Quelques résultats de Visik sur le problèmes elliptiques non linéaires par les méthodes de Minty-Browder.- J. Leray: Équations hyperboliques non-strictes: contre-exemples, du type de Giorgi aux théorèmes d'existence et d'unicité.- J. Leray, Y. Ohya: Equations et systèmes non-linéaires, hyperboliques non-stricts.- J. Leray, L. Waelbroeck: Norme formelle d'une fonction composée (préliminaires a l'étude des systèmes non linéaires, hyperbolique non stricts).- J. Moser: Some aspects of non-linear equations.- I. Segal: La variété des solutions d'une équation hyperbolique, non linéaire d'ordre 2.

Partial differential equations --- differentiaalvergelijkingen

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Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems that can be formulated for Keldysh-type equations, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is placed on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space, and specific applications to plasma physics, optics, and analysis on projective spaces are discussed.

Partial differential equations --- differentiaalvergelijkingen

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This set of lectures, which had its origin in a mini course delivered at the Summer Program of IMPA (Rio de Janeiro), is an introduction to intrinsic scaling, a powerful method in the analysis of degenerate and singular PDEs. In the first part, the theory is presented from scratch for the model case of the degenerate p-Laplace equation. This approach brings to light what is really essential in the method, leaving aside technical refinements needed to deal with more general equations, and is entirely self-contained. The second part deals with three applications of the theory to relevant models arising from flows in porous media and phase transitions. The aim is to convince the reader of the strength of the method as a systematic approach to regularity for this important class of equations.

Partial differential equations --- differentiaalvergelijkingen

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Il testo costituisce una introduzione alla teoria delle equazioni a derivate parziali, strutturata in modo da abituare il lettore ad una sinergia tra modellistica e aspetti teorici. La prima parte riguarda le più note equazioni della fisica-matematica, idealmente raggruppate nelle tre macro-aree diffusione, propagazione e trasporto, onde e vibrazioni. Nella seconda parte si presenta la formulazione variazionale dei principali problemi iniziali e/o al bordo e la loro analisi con i metodi dell'Analisi Funzionale negli spazi di Hilbert.

Partial differential equations --- differentiaalvergelijkingen