Open AccessGagliardo-Nirenberg-Sobolev inequalities on planar graphs
Author(s) -
Maria J. Esteban
Publication year - 2022
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2022051
Subject(s) - mathematics , nirenberg and matthaei experiment , sobolev space , planar , interpolation (computer graphics) , euler's formula , sobolev inequality , pure mathematics , set (abstract data type) , mathematical analysis , combinatorics , discrete mathematics , physics , computer science , motion (physics) , computer graphics (images) , classical mechanics , programming language
In this paper we study a family of the interpolation Gagliardo-Nirenberg-Sobolev inequalities on planar graphs. We are interested in knowing when the best constants in the inequalities are achieved. The inequalities being equivalent to some minimization problems, we also analyse the set of solutions of the Euler-Lagrange equations satisfied by extremal functions, or equivalently, by minimizers.