A Compact Course on Linear PDEs

Beschreibung

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 some basic results on Fredholm alternative and spectral theory, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, saddle point problems, parabolic equations and hyperbolic equations. Many 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 textbook is devoted to second order linear partial differential equations. The focus is on variational formulations in Hilbert spaces. It contains elliptic equations, including some basic results on Fredholm alternative and spectral theory, some useful notes on functional analysis, a brief presentation of Sobolev spaces and their properties, saddle point problems, parabolic equations and hyperbolic equations. Many 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.


It is a compact presentation of second order linear PDEs Variational formulations are fully described Include saddle-point formulation of elliptic PDEs

Autor*in

Alberto Valli

Themen in »A Compact Course on Linear PDEs«

Elliptic equations Saddle-point formulation Parabolic equations Hyperbolic equations Analysis Hilbert spaces partial differential equations

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“The book is designed to be compact, and it is – very. The author treats many topics very quickly, and the connecting links are also much abbreviated. A lot is demanded of the reader, even one starting with a background of classical PDEs at the undergraduate level.” (Bill Satzer, MAA Reviews, December 27, 2021)
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