Uniform Convexity in Variable Exponent Sobolev Spaces

Uniform Convexity in Variable Exponent Sobolev Spaces

We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1

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Veröffentlicht in:Symmetry (Basel) 2023-11, Vol.15 (11), p.1988
Hauptverfasser: Bachar, Mostafa, Khamsi, Mohamed A., Méndez, Osvaldo
Format: Artikel
Sprache:eng
Schlagworte:
Convexity
fixed point
Fredholm equations
Hilbert space
Inequality
modular function spaces
Norms
Partial differential equations
Sobolev space
variable exponent spaces
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Zusammenfassung:We prove the modular convexity of the mixed norm Lp(ℓ2) on the Sobolev space W1,p(Ω) in a domain Ω⊂Rn under the sole assumption that the exponent p(x) is bounded away from 1, i.e., we include the case supx∈Ωp(x)=∞. In particular, the mixed Sobolev norm is uniformly convex if 1
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15111988