Regularity of the extremal solutions in a Gelfand system problem
Craig Cowan
TL;DR
This paper investigates a Gelfand system and demonstrates that extremal solutions remain bounded when the system is sufficiently close to the scalar case, contributing to the understanding of solution regularity.
Contribution
It establishes boundedness of extremal solutions in Gelfand systems near the scalar case, extending known results to coupled systems.
Findings
Extremal solutions are bounded near the scalar case.
Boundedness depends on proximity to the scalar problem.
Provides conditions for regularity in Gelfand systems.
Abstract
We examine a Gelfand type system and show the extremal solutions are bounded provided we are close enough to the scalar case.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Nonlinear Differential Equations Analysis