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arXiv · 1605.00233

Sobolev subspaces of nowhere bounded functions

Pier Domenico Lamberti·Giorgio Stefani
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Abstract

We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elements are nowhere bounded functions. We also prove the existence of a closed infinite dimensional linear subspace whose non zero elements are nowhere $L^q$ functions for suitable values of $q$ larger than the Sobolev exponent.

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Pier Domenico Lamberti, Giorgio Stefani. 2016-05-01. Sobolev subspaces of nowhere bounded functions. https://arxiv.org/abs/1605.00233

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