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 Lq functions for suitable values of q larger than the Sobolev exponent.

Sobolev subspaces of nowhere bounded functions

LAMBERTI, PIER DOMENICO;STEFANI, GIORGIO
2016

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 Lq functions for suitable values of q larger than the Sobolev exponent.
2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3227598
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