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|Item type||Current location||Call number||Status||Date due||Barcode||Item holds|
|Monografia||Biblioteca Geral da Universidade do Minho||BGUM 517.95 - J||Checked out||2022-12-19||313423|
Intended for students who wish to get an introduction to the theory of partial differential equations, this text focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods and continuity methods. The book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations.