This is self-contained elementary introduction to partial differential equations. It assumes only advanced differential calculus and some Lp theory. Taking some basic physical models as a starting point, the author uses a classical analysis approach and a non-linear point of view to introduce the basic aspects of the theory and provide a background for some current research directions.
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This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.
Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.
The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations.
Reviews of the first edition:
The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs.
This is a well-written, self-contained, elementary introduction to linear, partial differential equations.
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