Sobolev spaces and approximation problems for differential operators
2001
In this paper we give an introduction to the theory of Sobolev spaces, and discuss the connection between these spaces and certain approximation problems associated with elliptic differential operators. In particular, we discuss uniform approximation by harmonic functions, mean approximation by solutions of elliptic equations, and the continuity of Dirichlet eigenvalues for an open set when the set is perturbed.
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