Böcker av Alberto Valli

This textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including the biharmonic problem, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, some basic results on Fredholm alternative and spectral theory, saddle point problems, parabolic and linear Navier-Stokes equations, and hyperbolic and Maxwell equations. Almost 80 exercises are added, and the complete solution of all of them is included. The work is mainly addressed to students in Mathematics, but also students in Engineering with a good mathematical background should be able to follow the theory presented here. This second edition has been enriched by some new sections and new exercises; in particular, three important equations are now included: the biharmonic equation, the linear Navier-Stokes equations and the Maxwell equations.

This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. It takes into account all the most used formulations, placing the problem in a rigorous functional framework.

Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs).