Sobolev Spaces and Partial Differential Equations

Basic information


45 hours


 PDE and Applications, Functional Analysis: Fundamentals, Functional Analysis: Linear Operators.


Hölder's spaces. Sobolev spaces: approximation, extension, features, Sobolev inequalities, compactness, Poincaré inequality, characterization by Fourier transform, Other spaces (negative Sobolev and spaces with time). Second Order Elliptical Equations: definition and weak solution. Existence of weak solution: Lax-Milgram; Energy Estimates; Fredholm alternative. Regularity. Maximum principle. Eigenvalues and self-functions.



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· Smoller, Joel; Reaction Diffusion Equations; Springer-Verlag.
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· LECUN, Yann; BENGIO, Yoshua; HINTON, Geoffrey. Deep learning. nature, v. 521, n. 7553, p. 436, 2015.