Open AccessImprovements on overdetermined problems associated to the $ p $-Laplacian
Author(s) -
Antonio Greco,
Francesco Pisanu
Publication year - 2022
Publication title -
mathematics in engineering
Language(s) - English
Resource type - Journals
ISSN - 2640-3501
DOI - 10.3934/mine.2022017
Subject(s) - overdetermined system , laplace operator , mathematics , operator (biology) , domain (mathematical analysis) , work (physics) , ball (mathematics) , calculus (dental) , pure mathematics , algebra over a field , mathematical analysis , engineering , mechanical engineering , chemistry , medicine , biochemistry , dentistry , repressor , transcription factor , gene
This work presents some improvements on related papers that investigate certain overdetermined problems associated to elliptic quasilinear operators. Our model operator is the $ p $-Laplacian. Under suitable structural conditions, and assuming that a solution exists, we show that the domain of the problem is a ball centered at the origin. Furthermore we discuss a convenient form of comparison principle for this kind of problems.