Abstract
The theory of Fourier series is used to develop the basic machinery of Sobolev spaces and prove the Sobolev embedding theorem. The embedding theorem and elliptic regularity for the Laplace operator is used to prove existence of solutions to the Dirichlet boundary problem.
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Einsiedler, M., Ward, T. (2017). Sobolev Spaces and Dirichlet’s Boundary Problem. In: Functional Analysis, Spectral Theory, and Applications. Graduate Texts in Mathematics, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-319-58540-6_5
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DOI: https://doi.org/10.1007/978-3-319-58540-6_5
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-58540-6
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