TY - JOUR
T1 - Reverse Stein-Weiss Inequalities on the Upper Half Space and the Existence of Their Extremals
AU - Chen, Lu
AU - Lu, Guozhen
AU - Tao, Chunxia
N1 - Publisher Copyright:
© 2019 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - The purpose of this paper is four-fold. First, we employ the reverse weighted Hardy inequality in the form of high dimensions to establish the following reverse Stein-Weiss inequality on the upper half space: for any nonnegative functions f 0 satisfying Second, we show that the best constant of the above inequality can be attained. Third, for a weighted system analogous to the Euler-Lagrange equations of the reverse Stein-Weiss inequality, we obtain the necessary conditions of existence for any positive solutions using the Pohozaev identity.
AB - The purpose of this paper is four-fold. First, we employ the reverse weighted Hardy inequality in the form of high dimensions to establish the following reverse Stein-Weiss inequality on the upper half space: for any nonnegative functions f 0 satisfying Second, we show that the best constant of the above inequality can be attained. Third, for a weighted system analogous to the Euler-Lagrange equations of the reverse Stein-Weiss inequality, we obtain the necessary conditions of existence for any positive solutions using the Pohozaev identity.
KW - Existence of Extremal Functions
KW - Pohozaev Identity
KW - Reverse Hardy-Littlewood-Sobolev Inequality
KW - Reverse Stein-Weiss Inequality
KW - Sharp Constants
KW - Stereographic Projection
UR - https://www.scopus.com/pages/publications/85060678313
U2 - 10.1515/ans-2018-2038
DO - 10.1515/ans-2018-2038
M3 - Article
AN - SCOPUS:85060678313
SN - 1536-1365
VL - 19
SP - 475
EP - 494
JO - Advanced Nonlinear Studies
JF - Advanced Nonlinear Studies
IS - 3
ER -