A Capacity Associated with the Weighted Lebesgue Space and Its Applications. (28th February 2022) - Li, Guoliang; Wang, Guanglan; Zhang, Lei
Abstract : In this paper, we focus on a further study of the weighted Lebesgue capacity associated with the following fractional heat equation: ∂ t + − Δ x α u t, x = 0,   ∀ α, t, x ∈ 0, 1 × 0, ∞ × ℝ n, u 0, x = f x,   ∀ x ∈ ℝ n . . More properties of that capacity are explored, and applications to a trace inequality for the weak solution of the equation are considered.