@article{Tumalun2023, 
author = {Nicky K. Tumalun and Philotheus E. A. Tuerah and Marvel G. Maukar and Anetha L. F. Tilaar and Patricia V. J. Runtu},
title = {An application of generalized Morrey spaces to unique continuation property of the quasilinear elliptic equations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {26007-26020},
keywords = {quasilinear elliptic equations, generalized Morrey spaces, Fefferman's inequality, bounded mean oscillation, strong unique continuation property},
url = {https://www.sciopen.com/article/10.3934/math.20231325},
doi = {10.3934/math.20231325},
abstract = {In this paper, we study nonnegative weak solutions of the quasilinear elliptic equation    div  (  A  (  x  ,  u  ,  ∇  u  )  )  =  B  (  x  ,  u  ,  ∇  u  ), in a bounded open set    Ω, whose coefficients belong to a generalized Morrey space. We show that    log  ⁡  (  u  +  δ  ), for    u a nonnegative solution and    δ an arbitrary positive real number, belongs to    BMO  (  B  ), where    B is an open ball contained in    Ω. As a consequence, this equation has the strong unique continuation property. For the main proof, we use approximation by smooth functions to the weak solutions to handle the weak gradient of the composite function which involves the weak solutions and then apply Fefferman's inequality in generalized Morrey spaces, recently proved by Tumalun et al. [1].}
}