Function spaces

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Department of Mathematics

Synopsis:

The lectures will be devoted to the study of function spaces with respect to applications in the theory of partial differential equations. The Lebesgue and Sobolev spaces will be introduced. The teorem about the density of smooth functions and the theorem about extending the operator from a dense subset will be proved. In addition, the Hausdorff measure will be introduced, and Lebesgue spaces on the boundary and non-integer order spaces will be defined. Proofs of embeddings, trace, inverse traces, and compact embeddings will be proved. Finally, we will show applications on elliptic problems.

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