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.
Citation
Pier Domenico Lamberti. Giorgio Stefani. "Sobolev Subspaces of Nowhere Bounded Functions." Real Anal. Exchange 41 (2) 367 - 376, 2016.