An existence result
Samy Skander Bahoura (IHP)
TL;DR
This paper proves the existence of changing-sign solutions for certain elliptic PDEs on compact Riemannian manifolds with specific curvature conditions, particularly for large dimensions.
Contribution
It establishes new existence results for elliptic PDE solutions on curved manifolds under curvature constraints, extending previous work to higher dimensions.
Findings
Existence of changing-sign solutions on compact Riemannian manifolds.
Solutions depend on curvature conditions and dimension.
Results hold for sufficiently large dimensions.
Abstract
On compact Riemannian manifold of dimension n, and under some conditions on the curvature, we have changing-sign solutions for n large enough for an elliptic PDE.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Elasticity and Material Modeling