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

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.

DOI : 10.1051/cocv/2020011
Classification : 35J35, 35J91, 35J92
Keywords: Bounded variation functions, 1-biharmonic operator, compactness with symmetry 
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     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},
     year = {2020},
     publisher = {EDP Sciences},
     volume = {26},
     doi = {10.1051/cocv/2020011},
     mrnumber = {4173853},
     zbl = {1460.35169},
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     url = {https://www.numdam.org/articles/10.1051/cocv/2020011/}
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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

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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.