Gagliardo-Nirenberg-Sobolev inequalities on planar graphs
Maria J. Esteban (CEREMADE)
TL;DR
This paper investigates Gagliardo-Nirenberg-Sobolev inequalities on planar graphs, focusing on the existence of optimal constants and analyzing solutions to related Euler-Lagrange equations.
Contribution
It provides new insights into the conditions for achieving best constants and characterizes solutions on planar graphs.
Findings
Conditions for best constant achievement identified
Solutions to Euler-Lagrange equations characterized
Implications for interpolation inequalities on graphs
Abstract
In this paper we study a family of interpolation Gagliardo-Nirenberg-Sololev inequalities on planar graphs. We are interested in knowing when the best constants in the inequalities are achieved. We also analyse the set of solutions of the corresponding Euler-Lagrange equations.
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Taxonomy
TopicsDiverse Research Studies Overview