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

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
Settore MAT/05 - Analisi Matematica
Nowhere bounded functions; Sobolev Embedding; Sobolev spaces; Analysis; Geometry and Topology
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79100
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