The book takes an intriguing mixed approach to partial differential equations, shining a modern light on a classic topic Many motivations and examples enlighten the interplay between modelling and theory Includes both a modelling approach and mathematical techniques for proving rigorous existence and regularity results

Autorentext

Sandro Salsa is a Emeritus Professor of Mathematical Analysis at Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on boundary behavior, regularity and free boundary problems. He is an author of 14 books and several papers in the most prestigious scientific mathematical journals. Gianmaria Verzini is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan. He is author of 5 books and more than 50 papers, published on prominent international journals. His scientific interests concern the applications of Nonlinear Analysis to the existence, multiplicity, qualitative properties and regularity of solutions to nonlinear differential equations and systems.

Inhalt

1 Introduction.- 2 Diffusion.- 3 The Laplace Equation.- 4 Scalar Conservation Laws and First Order Equations.- 5 Waves and Vibration.- 6 Elements of Functional Analysis.- 7 Distributions and Sobolev Spaces.- 8 Variational Formulation of Elliptic Problems.- 9 Weak Formulation of Evolution Problems.- 10 More Advanced Topics.- 11 Systems of Conservation Laws.- Appendix A: Measures and Integrals.- Appendix B: Identities and Formulas.