Geodesic
Optimal integrability for some integral system of Wolff type
Filomat, Tome 35 (2021) no. 9, p. 2951

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DOI

In the paper, we obtain the optimal integrability for positive solutions of the following integral system involving Wolff potentials:        u(x) = W β,γ (v q)(x), x ∈ R n , v(x) = W β,γ (u p)(x), x ∈ R n , where p, q > 0, β > 0, γ > 1 and 0 βγ n. Ma, Chen and Li [Advances in Mathematics, 226(2011), 2676-2699] developed the regularity lifting method and obtained the optimal integrability for p > 1, q > 1. Here, based on some new observations, we overcome the difficulty there, and derive the optimal integrability for the case of p > 0, q > 0 and pq > 1. This integrability plays a key role in estimating the asymptotic behavior of positive solutions
DOI : 10.2298/FIL2109951L
Classification : 45E10, 45G05
Keywords: Wolff potential, Regularity liftings, optimal integrability interval 
Ling Li. Optimal integrability for some integral system of Wolff type. Filomat, Tome 35 (2021) no. 9, p. 2951 . doi: 10.2298/FIL2109951L
@article{10_2298_FIL2109951L,
     author = {Ling Li},
     title = {Optimal integrability for some integral system of {Wolff} type},
     journal = {Filomat},
     pages = {2951 },
     year = {2021},
     volume = {35},
     number = {9},
     doi = {10.2298/FIL2109951L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2109951L/}
}
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