Abstract
This chapter is devoted to studying boundary value problems for second-order elliptic equations. The variational (also known as Hilbert space) approach to the Dirichlet problem is emphasized. Maximum principles are discussed in §5.10 and §5.11, which are independent of the preceding sections and are essential reading along with §5.1, §5.2, and §5.3. Sections 5.8 and 5.9 address the technically difficult question of the regularity of the weak solution constructed in §5.3. Sections 5.4—5.7 treat a variety of topics which rely solely on the H1 variational approach to the Dirichlet problem. It is interesting that this straightforward argument propels one so far.
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© 1991 Springer Science+Business Media New York
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Rauch, J. (1991). The Dirichlet Problem. In: Partial Differential Equations. Graduate Texts in Mathematics, vol 128. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0953-9_5
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DOI: https://doi.org/10.1007/978-1-4612-0953-9_5
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