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A Note on the Differential Operator Δ2+a(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2020年03期
Page:
7-11
Research Field:
·数学·
Publishing date:

Info

Title:
A Note on the Differential Operator Δ2+a
Author(s):
Dai Shaoyu1; Pan Yifei2
(1.Jingling Institute of Technology,Nanjing 211169,China)(2.Purdue University Fort Wayne,Fort Wayne 46805,USA)
Keywords:
Hormander L2 method; weighted Hilbert space; differential operator
PACS:
O177.92
DOI:
10.3969/j.issn.1001-4616.2020.03.002
Abstract:
Using Hormander L2 method for Cauchy-Riemann equations from complex analysis,we study a simple differential operator Δ2+a in weighted Hilbert space L2(R2,e-|x|2). We prove the existence of global weak solutions of the equation about the differential operator and the existence of a right bounded inverse of the differential operator.

References:

[1] HORMANDER L. L2 estimates and existence theorems for the operator[J]. Acta mathematica,1965,113:89-152.
[2]ADACHI K. Several complex variables and integral formulas[M]. Singapore:World Scientific Publishing Co. Pte. Ltd,2007:53-99.
[3]KRANTZ S G. Function theory of several complex variables[M]. 2nd ed. Rhode Island:American Mathematical Society,2001:175-194.
[4]EVANS L C. Partial differential equations[M]. Rhode Island:American Mathematical Society,1998:23-25.
[5]DAI S Y,LIU Y,PAN Y F. A right inverse of differential operator Δ+a in weighted Hilbert space L2(Rn,e-|x|2)[J/OL]. Arxive-prints,2019:1909.12477v1.

Memo

Memo:
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Last Update: 2020-09-15