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Elliptic Equations

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Book cover Problems on Partial Differential Equations

Part of the book series: Problem Books in Mathematics ((PBM))

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Abstract

This chapter is devoted to the study of elliptic equations. We begin with classical theory of harmonic functions, and then the modern approach to weak solutions (variational approach, Lax–Milgram’s Lemma) is introduced.

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References

  1. B. Dacorogna. Direct methods in the calculus of variations, volume 78 of Applied Mathematical Sciences. Springer, New York, second edition, 2008.

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  2. L. C. Evans. Partial differential equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition, 2010.

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Borodzik, M., Goldstein, P., Rybka, P., Zatorska-Goldstein, A. (2019). Elliptic Equations. In: Problems on Partial Differential Equations. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-14734-1_4

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