Yang Liu

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20132021

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math.AP2021

$L^{2}$ estimate for polynomials of the Laplace operator with Gaussian measure

Shaoyu Dai, Yang Liu, Yifei Pan

Let $P (Δ)$ be a polynomial of the Laplace operator $Δ = \sum_{j = 1}^{n} \frac{\partial ^{2}}{\partial x _{j}^{2}}$ on $R^{n}$ . We prove the existence of weak solutions of the equation $P(…

math.AP2019

A right inverse of differential operator $Δ + a$ in weighted Hilbert space $L^{2} (R^{n}, e^{- ∣ x ∣^{2}})$

Shaoyu Dai, Yang Liu, Yifei Pan

In this note, we prove the existence of weak solutions of a Poisson type equation in the weighted Hilbert space $L^{2} (R^{n}, e^{- ∣ x ∣^{2}})$ .

math.AP2013

A variant of Hörmander's $L^{2}$ theorem for Dirac operator in Clifford analysis

Yang Liu, Zhihua Chen, Yifei Pan

In this paper, we give the Hörmander's $L^{2}$ theorem for Dirac operator over an open subset $Ω \in R^{n + 1}$ with Clifford algebra. Some sufficient condition on the existence of the…

L2 estimate for polynomials of the Laplace operator with Gaussian measure

A right inverse of differential operator Δ+a in weighted Hilbert space L2(Rn,e−∣x∣2)

A variant of Hörmander's L2 theorem for Dirac operator in Clifford analysis

$L^{2}$ estimate for polynomials of the Laplace operator with Gaussian measure

A right inverse of differential operator $Δ + a$ in weighted Hilbert space $L^{2} (R^{n}, e^{- ∣ x ∣^{2}})$

A variant of Hörmander's $L^{2}$ theorem for Dirac operator in Clifford analysis