Partial Differential Equations

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The book serves as a comprehensive graduate-level introduction to partial differential equations, detailing the foundational mathematical problems related to elliptic, parabolic, and hyperbolic types. It examines the interconnections among these equations and includes discussions on Brownian motion and pattern formation. The second section emphasizes existence schemes and solution estimates, covering essential topics like Sobolev space theory, weak and strong solutions, and Moser iteration, equipping readers with techniques relevant to contemporary research in elliptic equations.