Partial Differential Equations by Lawrence C. Evans
A rigorous graduate-level introduction to the theory and methods for linear and nonlinear partial differential equations, emphasizing existence, uniqueness, regularity, and qualitative behavior of solutions; it develops the functional-analytic framework of distributions and Sobolev spaces, energy and variational methods, and tools such as the maximum principle, fundamental solutions, and a priori estimates. The text treats elliptic, parabolic, and hyperbolic equations in depth, proving key results like Lax–Milgram, Schauder and Calderón–Zygmund estimates, and interior and boundary regularity, and introduces modern techniques including viscosity solutions for first-order and fully nonlinear problems. Rich with examples, exercises, and detailed proofs, it balances abstract theory with applications to classical PDEs such as the Poisson, heat, and wave equations and provides a foundation for further study in analysis and applied mathematics.
- Published
- 1998
- Nationality
- American
- Length
- Unknown
- Pages
- 600-700 pages
- Original Language
- English
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