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Global regularity estimates for a class of quasilinear elliptic equations in the whole space.
- Source :
-
Nonlinear Analysis . May2020, Vol. 194, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- In this paper we use the Hardy–Littlewoodmaximal functions to obtain the following global BMO estimates f ∈ B M O (R n) ⇒ ∇ u ∈ B M O (R n) for the weak solutions of a class of quasilinear elliptic equations div a ∇ u ∇ u = div f in R n , where B (t) = ∫ 0 t τ a (τ) d τ for t ≥ 0. Meanwhile, we use the iteration-covering procedure to prove that B f ∈ L q (R n) ⇒ B ∇ u ∈ L q (R n) for any q > 1 for the weak solutions of div a ∇ u ∇ u = div a f f in R n. Moreover, we remark that a (t) = t p − 2 (p -Laplace equation) and a (t) = t p − 2 log (1 + t) satisfy the given conditions in this work. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ESTIMATES
*ELLIPTIC equations
Subjects
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 194
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 142003651
- Full Text :
- https://doi.org/10.1016/j.na.2018.07.004