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.

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
File in questo prodotto:
File Dimensione Formato  
preprint.pdf

accesso aperto

Tipologia: Submitted version (pre-print)
Licenza: Solo Lettura
Dimensione 361.46 kB
Formato Adobe PDF
361.46 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/79100
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact