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In this paper we prove the compactness of the embeddings of the space of radially symmetric functions of BL(ℝ$$) into some Lebesgue spaces. In order to do so we prove a regularity result for solutions of the Poisson equation with measure data in ℝ$$, as well as a version of the Radial Lemma of Strauss to the space BL(ℝ$$). An application is presented involving a quasilinear elliptic problem of higher-order, where variational methods are used to find the solutions.
@article{COCV_2020__26_1_A86_0,
author = {Hurtado, Elard J. and Pimenta, Marcos T.O. and Miyagaki, Olimpio H.},
title = {On a quasilinear elliptic problem involving the 1-biharmonic operator and a {Strauss} type compactness result},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2020011},
mrnumber = {4173853},
zbl = {1460.35169},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2020011/}
}
TY - JOUR AU - Hurtado, Elard J. AU - Pimenta, Marcos T.O. AU - Miyagaki, Olimpio H. TI - On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2020011/ DO - 10.1051/cocv/2020011 LA - en ID - COCV_2020__26_1_A86_0 ER -
%0 Journal Article %A Hurtado, Elard J. %A Pimenta, Marcos T.O. %A Miyagaki, Olimpio H. %T On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2020011/ %R 10.1051/cocv/2020011 %G en %F COCV_2020__26_1_A86_0
Hurtado, Elard J.; Pimenta, Marcos T.O.; Miyagaki, Olimpio H. On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 86. doi : 10.1051/cocv/2020011. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2020011/
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Cité par Sources :
E.J. Hurtado has been supported by CAPES 001, M.T.O. Pimenta by FAPESP 2019/14330-9 and CNPq 303788/2018-6 and O.H. Miyagaki by CNPq 307061/2018-3 and INCTMAT/CNPq/Brazil.