Elliptic Regularity Theory by Approximation Methods

Edgard A. Pimentel is Research Scientist at the University of Coimbra and Assistant Professor of Mathematics at Pontifical Catholic University of Rio de Janeiro. He is researcher for the National Council of Science and Technology (CNPq-Brazil), a junior associate fellow of the International Centre for Theoretical Physics, and an affiliated member of the Brazilian Academy of Sciences.

• Preface; 1. Elliptic partial differential equations; 2. Flat solutions are regular; 3. The recession strategy; 4. A regularity theory for the Isaacs equation; 5. Regularity theory for degenerate models; References; Index.

'The regularity theory of elliptic partial differential equations is one of the bedrocks of modern mathematics since it elegantly and creatively uses virtually all possible mathematical tools to construct a solid set of concepts with ubiquitous applications. This book tells a story about this regularity theory, especially from the point of view of viscosity solutions for fully nonlinear equations and in the light of perturbative methods. As all good stories, the important part is not the happy ending in itself, but the whole plot through the series of adventures and vicissitudes (namely, the beautiful theorems) in which the reader will be captured page after page.' Enrico Valdinoci, University of Western Australia