A Capacity Associated with the Weighted Lebesgue Space and Its Applications

A Capacity Associated with the Weighted Lebesgue Space and Its Applications

In this paper, we focus on a further study of the weighted Lebesgue capacity associated with the following fractional heat equation: ∂t+−Δxαut,x=0, ∀α,t,x∈0,1×0,∞×ℝn,u0,x=fx, ∀x∈ℝn.. More properties of that capacity are explored, and applications to a trace inequality for the weak solution of the eq...

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Veröffentlicht in:Journal of function spaces 2022, Vol.2022, p.1-11
Hauptverfasser: Li, Guoliang, Wang, Guanglan, Zhang, Lei
Format: Artikel
Sprache:eng
Schlagworte:
Inequality
Thermodynamics
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Beschreibung
Zusammenfassung:In this paper, we focus on a further study of the weighted Lebesgue capacity associated with the following fractional heat equation: ∂t+−Δxαut,x=0, ∀α,t,x∈0,1×0,∞×ℝn,u0,x=fx, ∀x∈ℝn.. More properties of that capacity are explored, and applications to a trace inequality for the weak solution of the equation are considered.
ISSN:2314-8896
2314-8888
DOI:10.1155/2022/1257963