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Lectures on Linear Partial Differential Equations
The first three chapters are on elementary distribution theory and Sobolev spaces with many examples and applications to equations with constant coefficients.
The following chapters study the Cauchy problem for parabolic and hyperbolic equations, boundary value problems for elliptic equations, heat trace asymptotics, and scattering theory. The book also covers microlocal analysis, including the theory of pseudodifferential and Fourier integral operators, and the propagation of singularities for operators of real principal type.
Among the more advanced topics are the global theory of Fourier integral operators and the geometric optics construction in the large, the Atiyah-Singer index theorem in math, and the oblique derivative problem.
Publisher: American Mathematical Society (July 6, 2011)
Language: English
ISBN-10: 0821852841
ISBN-13: 978-0821852842
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