JournalszaaVol. 30, No. 1pp. 59–69

An Example of a Functional which is Weakly Lower Semicontinuous on W01,pW_0^{1,p} for every p>2p>2 but not on H01H_0^1

  • Fernando Farroni

    Università Telematica Pegaso, Napoli, Italy
  • Raffaella Giova

    Università degli Studi di Napoli Parthenope, Italy
  • François Murat

    Université Pierre et Marie Curie, Paris, France
An Example of a Functional which is Weakly Lower Semicontinuous on $W_0^{1,p}$ for every $p>2$ but not on $H_0^1$ cover
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Abstract

In this note we give an example of a functional which is defined and coercive on H01(Ω)H^1_0(\Omega), which is sequentially weakly lower semicontinuous on W01,p(Ω)W^{1,p}_0(\Omega) for every p>2p>2, but which is not sequentially lower semicontinuous on H01(Ω)H^{1}_0(\Omega). This functional is non local.

Cite this article

Fernando Farroni, Raffaella Giova, François Murat, An Example of a Functional which is Weakly Lower Semicontinuous on W01,pW_0^{1,p} for every p>2p>2 but not on H01H_0^1. Z. Anal. Anwend. 30 (2011), no. 1, pp. 59–69

DOI 10.4171/ZAA/1423