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On optimal [formula omitted] estimates for [formula omitted]-Laplace type equations.
- Source :
-
Nonlinear Analysis . Nov2020, Vol. 200, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- In this paper, we investigate the optimal C 1 , α estimates for the elliptic p (⋅) -Laplace equation: div (a (x) | ∇ u | p (x) − 2 ∇ u) = div h (x) + f (x) in Ω with f ∈ L q (⋅) (Ω) and a , h ∈ C σ (Ω ¯). Based on a certain geometric oscillation estimate, the scaling arguments and appropriate localization technique as well as the careful analysis on the variable exponents, we exhibit how the optimal Hölder exponent of ∇ u is influenced by p (⋅) , q (⋅) and σ. This work can be regarded as a natural follow up to the paper by Araújo and Zhang (in press). [ABSTRACT FROM AUTHOR]
- Subjects :
- *ESTIMATES
*EQUATIONS
*ELLIPTIC equations
*EXPONENTS
*OSCILLATIONS
*ARGUMENT
Subjects
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 200
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 145443043
- Full Text :
- https://doi.org/10.1016/j.na.2020.112030