Weighted inequality theory for fractional integrals is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes. Basic weighted inequalities are often associated to Hardy, Littlewood and Sobolev [6, 11], Caffarelli, Kohn and Nirenberg [4], respectively to Stein and Weiss [12]. A key attempt in the present paper is to prove a Stein–Weiss inequality with lack of symmetry and variable exponents. We quantify the defect of symmetry of the potential by considering the gap between the minimum and the maximum of the variable exponent. We conclude our work with a section dealing with the existence of stationary waves for a class of nonlocal problems with Choquard nonlinearity and anisotropic Stein–Weiss potential.
Accepté le :
Publié le :
Youpei Zhang 1, 2 ; Xianhua Tang 2 ; Vicenţiu Rădulescu 1, 3

@article{CRMATH_2021__359_8_959_0, author = {Youpei Zhang and Xianhua Tang and Vicen\c{t}iu R\u{a}dulescu}, title = {Anisotropic {Choquard} problems with {Stein{\textendash}Weiss} potential: nonlinear patterns and stationary waves}, journal = {Comptes Rendus. Math\'ematique}, pages = {959--968}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {8}, year = {2021}, doi = {10.5802/crmath.253}, language = {en}, }
TY - JOUR AU - Youpei Zhang AU - Xianhua Tang AU - Vicenţiu Rădulescu TI - Anisotropic Choquard problems with Stein–Weiss potential: nonlinear patterns and stationary waves JO - Comptes Rendus. Mathématique PY - 2021 SP - 959 EP - 968 VL - 359 IS - 8 PB - Académie des sciences, Paris DO - 10.5802/crmath.253 LA - en ID - CRMATH_2021__359_8_959_0 ER -
%0 Journal Article %A Youpei Zhang %A Xianhua Tang %A Vicenţiu Rădulescu %T Anisotropic Choquard problems with Stein–Weiss potential: nonlinear patterns and stationary waves %J Comptes Rendus. Mathématique %D 2021 %P 959-968 %V 359 %N 8 %I Académie des sciences, Paris %R 10.5802/crmath.253 %G en %F CRMATH_2021__359_8_959_0
Youpei Zhang; Xianhua Tang; Vicenţiu Rădulescu. Anisotropic Choquard problems with Stein–Weiss potential: nonlinear patterns and stationary waves. Comptes Rendus. Mathématique, Volume 359 (2021) no. 8, pp. 959-968. doi : 10.5802/crmath.253. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.253/
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