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An end point Orlicz type estimate for nonlinear elliptic equations.
- Source :
-
Nonlinear Analysis . Dec2018 Part B, Vol. 177, p572-585. 14p. - Publication Year :
- 2018
-
Abstract
- Abstract We study nonlinear elliptic equations of p -Laplacian type in divergence form to establish a natural Calderón–Zygmund type theory of an Orlicz space type, where the Lebesgue space is the special case with Φ (t) = t q p : Φ (| F | p) ∈ L 1 (Q 2 R) ⟹ Φ (| D u | p) ∈ L 1 (Q R). In the previous results, the estimates obtained were strictly above the natural exponents, and the function such as Φ (t) = t log (1 + t) was ruled out for the candidate of Φ. But with our approach, Φ can be selected up to the end point case of the estimates, and the functions Φ (t) = t and Φ (t) = t log (1 + t) can be additionally selected for Φ. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0362546X
- Volume :
- 177
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 132782538
- Full Text :
- https://doi.org/10.1016/j.na.2018.03.014